From: "Gerald K. Dobiasovsky" Subject: Re: (fractint) Fractint Development: The Ljapunow Type Date: 02 Apr 2001 00:11:27 +0200 Guy Marson wrote: > Hi fractinters, > > Does somebody know the Lyapunow-formula written for the Parser similar to > the build-in type, or a place (url or so) to find this formula? > > Cheers, > > Guy Hi, Since I have never seen such a beast (although the parser can be coaxed to do astounding things, as all the formulas by Sylvie Gallet, Damien Jones, Paul Carlson etc. are proof of), I feel obliged to post my construct. A word of caution is in order here. This thing is not exactly user friendly for a couple of reasons (some are: the original was written when there existed no if- statements, the parser supported only much smaller formulas, and *I* know what all those variables are supposed to achieve - or at least I think I do ;-)). Some explanations: (Parameter names in the formula comments are written in the form: p# ... real part / imaginary part) The ab-String is input the same way as in Fractint's Lyapunov type, converting a's to 1's and b's to 0's, but *without* dropping the leading a and the trailing b!!! In fact there's no need to rotate the string at all, it may have leading b's; the length of the string is input in a separate variable (abMax). Scaling Exponent and Scaling Factor are used to bring the output into the appropriate color range (a bit of fiddling around is necessary here). Filter Cycles does the same as Fractint's Lyapunov parameter. Bailout is used to catch possible overflows of the iteration function. Fractint is very good at catching those itself (at first my formula ended in the statement "n == n", letting all pixels iterate maxiter times and leaving it to Fractint what happened to those values that grew too big), only it insisted on painting those pixels with a different color than those with non-overflowing, but still positive Lyapunov exponents. Zero Level: Normally all pixels with a positive result are painted as one color value, those with negative values are mapped onto the whole color map. Due to small calculation errors, pixels with results near zero end up "on the wrong side of the dividing line" (using lyapunov.map and assigning black as background one sometimes gets black spots in otherwise yellow areas or yellow "junk" in areas that should be background). This parameter moves the "dividing line", by setting it to e.g. -10 all values (-10 < value < 0) will be painted as background. (Note: This test is done *before* the value is divided by the number of iterations!) Divergence Result: This is the value (*not* the color number!) of background pixels returned to Fractint to map it onto the loaded color map. Quite a bit of fiddling is needed here, too, because every change of the number of iterations needs a recalibration of this parametrer for getting the same color output as before (did I point out this formulas not being user friendly? ;-)) Further notes: One doesn't need to set logmap=1 (as is done in the accompanying pars), but if one does, maxiter has to be set to at least 256 or not all colors of the color map can be reached (=displayed). Fractint iterates its Lyapunov type differently from these formula implementations (if one has a string of "aab" then Fractint iterates its Lyapunov three times for each iteration set as maxiter - two time because of the two a's, one time for the lone b; in the formula parser each iteration is *one* loop using *one* string token, of course). Well, I hope you will have fun with formulas nevertheless and I better stop now before this posting grows bigger still. Regards, Gerald ---------------- cut here, save as .par file ------------------ Lyapunov {;Parser version of Fractint's Lyapunov formula ; reset=2001 type=formula formulaname=Lyapunov corners=0/6/0/4.5 params=0.66/3/1/0.5/0.35/100/10/1.4/1000000 float=y maxiter=1000 inside=zmag outside=255 logmap=yes periodicity=0 colors=@lyapunov.map } LyapSqrSinR {;Lyapunov-Fractal of "Do-It-Yourself"-Formula ; reset=2001 type=formula formulaname=LyapSqrSinR corners=0.006343064/3.837554/-0.09798406/3.733226 params=2.5/1.5/3/1/0.5/0.55/10/100/1000000/1.4 float=y maxiter=1000 inside=zmag outside=255 logmap=yes periodicity=0 colors=@lyapunov.map } frm:Lyapunov {;"standard" Lambda-Formula ; ;abMax = Length of ab-string in the form of: 2^LENGTH - 1 ;periodicity=no, inside=zmag, outside=ColorNumber ; ;p1 ... Starting Value / abMax ;p2 ... ab-String / Scaling Exponent ;p3 ... Scaling Faktor / Filter Cycles ;p4 ... Zero Level / Divergence Result ;p5 ... Bailout ; x = real(p1), max = imag(p1), ab = real(p2) se = imag(p2), sk = real(p3) n = imag(p3), z = imag(p4) mxi = n + 1 - maxit sum = 0: n = n - 1 ab = 2*ab IF (ab > max) ab = ab - max c = imag(pixel) ELSE c = real(pixel) ENDIF IF (n < 0) sum = sum + log(abs(c*(1-2*x))) IF (n <= mxi && sum < p4) z = (sum/n)^se*sk ENDIF ENDIF x = c*x*(1-x) p5 >= abs(x) } frm:LyapSqrSinR {;Function a*(sin(x+r))^2 ; ;ab-String: Swapping of r between two values ;abMax = Length of ab-string in the form of: 2^LENGTH - 1 ;periodicity=no, inside=zmag, outside=ColorNumber ; ;p1 ... Factor a / Starting Value ;p2 ... abMax / ab-String ;p3 ... Scaling Exponent / Scaling Faktor ;p4 ... Zero Level / Filter Cycles ;p5 ... Bailout / Divergence Result ; a = real(p1), x = imag(p1) max = real(p2), ab = imag(p2) se = real(p3), sk = imag(p3) n = imag(p4), z = imag(p5) mxi = n + 1 - maxit a2 = 2*a, sum = 0: n = n - 1 ab = 2*ab IF (ab > max) ab = ab - max r = imag(pixel) ELSE r = real(pixel) ENDIF xpr = x + r, sxpr = sin(xpr) IF (n < 0) sum = sum + log(abs(a2*sxpr*cos(xpr))) IF (n <= mxi && sum < p4) z = (sum/n)^se*sk ENDIF ENDIF x = a*sqr(sxpr) p5 >= abs(x) } ----------------------- end of .par --------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) Fractint Development Date: 02 Apr 2001 15:02:06 -0000 >From: "Jonathan Osuch" >Reply-To: fractint@lists.xmission.com >To: >Subject: Re: (fractint) Fractint Development >Date: Thu, 29 Mar 2001 19:33:11 -0600 > >I am currently working on the true color support for the DOS version. >There >seems to be a problem with the routines that Bert Tyler added. At any >rate, >I'm having difficulty getting the images to appear correctly colored on the >screen. I'll let you know when it is fixed. Hmm... I know those routines were there (there's some debug option that makes type=test do some truecolour stuff). I always wondered what the deal was with that... >The memory limitations stem from two sources. One is that Fractint is >compiled in the medium memory model. This means that memory usable for >near >data is limited to 64KB unless some form of swapping is done. This memory >includes the stack space, and we are banging up against this limit >constantly. And, no it isn't a simple matter to just change the memory >model. So, you mean that FractInt can as such only use 64KB of memory? Are you saying that if you *did* change the memory model this would magically make everything better? (I must confess to not knowing what a "memory model" is. I presume it's something to do with the size of the memory address references or something...) What's involved in such a change? Is it just a case of going through the program and changing half a million lines of code on a find-and-replace basis, or does it require an actaul redesign of the code? I'd really prefer FractInt to remain a DOS program, or perhaps to have a DOS *and* a Windows version. (...and a Linux/UNIX version, like they do with POV-Ray. Hey... isn't that a Stone Soup project too?) >The other problem is that we do indeed use extended and/or expanded >memory for options other than just disk video. Saving the on screen image >when switching to a menu comes to mind. If you had more memory to play with, could this be avoided? (I understand that disk video can use insane quantities of RAM, but keeping a copy of the video buffer for a normal screen shouldn't be too bad...) >I'll let all the other developer's respond to your question themselves. Hmm... they seem rather quiet so far... An the basis that quiet implies busy, this may well be a good sign 8-) >Jonathan Thanks for the information! Andrew. _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) FOTD 03-04-01 (Many Happy Returns [5]) Date: 02 Apr 2001 21:47:12 EDT Classic FOTD -- April 03, 2001 (Rating 5) Fractal visionaries and enthusiasts: Today, the FOTD returns after its 1-1/2 week hiatus, with the first fractal I've calculated in that time. Of course, this is the reason I have named it "Many Happy Returns. The average rating of 5 reflects my opinion of my first fractal effort in 11 days. The conditions here at the new Fractal Central auxiliary are still a bit hectic, but they are becoming more organized every day. In fact, the organization is such that I almost know where everything is located. Unfortunately, I still lack the time for the long philosophical discussions that have made the FOTD what it is :-/ but as things gradually return to normal in the near future, the FOTD discussions will become longer and more complex, until hopefully we finally solve the mystery of the universe. :-\ Today's image however is no mystery. It was created by combining small negative portions of Z^(-1.2) and Z^(-12). It's one of those moth-eaten images so full of holes that the holes are more interesting than the midget at the center. Since my DSL internet connection is not yet established, the GIF images are not yet being posted to Usenet, but hopefully Paul and Scott have posted today's image to their web sites at: and at: The fractal weather today was mostly cloudy and a chilly 50F (10C) -- conditions that combined with a brisk wind to keep the fractal cats indoors sulking most of the afternoon. I eased their distress with a treat of tuna. I see it's time to do a little more organizing, but I'll return in another 24 hours with another fractal. Until then, take care, and the fractals will keep getting better. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Many_Happy_Returns { ; time=0:29:18.22--SF5 on a p200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.02268278481078340/-0.001079531652657\ 37/1.821185e+009/1/-127.5 params=12/-1.2/1/-12/-1.15/800 float=y maxiter=2500 inside=0 logmap=380 periodicity=10 colors=000bmiblhbkgajgaifaieahdagc`fc`eb`da`d``c__\ b__aZ_`Y__X__XYZWWZVVZUTYTRYSQYROXQMXPLXPKZQJ_QI`Q\ HaRGbRFcREeSDfSCgSChSBiTAjT9kT8mU7nU6oU5pV4qV3rV3s\ V5nR7iO8dLA_IBVFDQCEM9DOADQADRACTBCUBCWBBXCBZCB_CB\ aCAcDAdDAfD9gE9iE9jE8lF8mF8oF8pF9oGAnGBnHCmHDlHElI\ FkIGkJHjJIiJJiKKhKLgKMgLNfLOfMPeMQdMRdNScNScNRdMQe\ MPeMOfMOfMNgMMhMLhLKiLKiLJjLIkLHkLGlLGlLHkKHkKkr9h\ oCflFdiIafL_cOY`RVYUTVXRR_OObMLeKIhHFkFCnD9qA6t83w\ 60yDGqKVjQicTafVViYOl_Hoa8taAqaCoaEmaGjaIhaKfaMcaO\ aaP_aRXaTVaVTaXQaZOa`MabJadHSt_aeFfhLjjRnmXpt`qqar\ obsmbskcticugduedvbew`fxZfxXgyVgzThzRhxRewRbvR`uRY\ tRWsRTqRRpROoRMnRJmRHlREjO8kQAkRClSElUGmVImWKnXMnZ\ On_Qo`SoaUpcWpdYqe_qfaqhcrierjgskismktnmtootpqpoom\ nnjmlglkdljakhZjgVieShdPhcMgaJf`GeaDdbAdcBcdBceBcf\ BcgCchCciCcjCckDclDcmDcnDcoEcpEcqEcrEcsCctEcuGcvIc\ wKcxMcyOczQczSczUczWczYcz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Michael Weitzel Subject: Re: (fractint) Fractint Development: The Ljapunow Type Date: 01 Apr 2001 13:27:19 +0200 Am Sonntag, den 01. April 2001, um 00:44h schrieb Guy Marson: > Does somebody know the Lyapunow-formula written for the Parser similar to > the build-in type, or a place (url or so) to find this formula? I'm not an expert ... but ... Ljapunow diagrams are based on simple population models (for yeast for example) or other oscillating systems. In the beginning (time t=0) of the experiment you start with x[t] = x[0] individuals. The number x[t+1] of individuals in generation t+1 is proportional to the number x[t] in generation t (the generation before) and the food which is given by the environment (and/or was left over by former generations) and other environmental parameters - all together expressed through r: x[t+1] ~ x[t] x[t+1] ~ r Fractint uses the "logistic equation" to determine this number: x[t+1] = r * x[t] * (1 - x[t]) For the calculation of Ljapunow diagrams the parameter r ist changed periodically in a predefined way - to A or to B. The sequence of A's and B's defines the rules of the game: For example ABB results in ...BABBABBABBABBABBA... . The screen shows an A-B-plane. If the sequence says, that r=B - you have to set r to the B-coordinate of your current pixel... if it says r=A the A-coordinate is used. The formula is iterated a few hundred times ... so that the influence of the starting value x[0] decreases more and more. Then the calculation continues another few hundred/thousand times and while iterating the Ljapunow exponent lambda is calculated (see literature, characterizes the averange error-growth in the neighborhood of x[0]) using the simplification that ln(a*b*c) = ln(a)+ln(b)+ln(c) (which protects the floating point numbers from overflow): 1 | En | lambda(x[0]) = --- ln|----| n | E0 | | En | | En | | En-1 | | E1 | with total error amplification : |----| = |------|*|------|*...*|----| | E0 | | En-1 | | En-2 | | E0 | | Ea | d f(x[a-1]) |------| can be expressed as ----------- | Ea-1 | d x[a-1] n n 1 --- |d (r*x[i]*(1-x[i]))| 1 --- lambda(x[0]) = --- \ ln|-------------------| = --- \ ln|r*(1-2*x[i])| n / | d x[i] | n / --- --- i=0 i=0 If you use your "natural" screen coordinates (for ex.: x=0...1023, y=0..767) you probably won't see anything on your screen. You can see Fractint's corner parameters if you press [Tab]. -- Michael LDKnet / LDK/LUG / Unix-AG *Weitzel* /LinuX --- email: michael(at)ldknet.org Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Michael Weitzel Subject: Re: (fractint) Fractint Development: The Ljapunow Type Date: 03 Apr 2001 12:47:55 +0200 Am Montag, den 02. April 2001, um 00:11h schrieb Gerald K. Dobiasovsky: > > Does somebody know the Lyapunow-formula written for the Parser similar to > > the build-in type, or a place (url or so) to find this formula? [your frm + par files] sorry ... probably a misunderstanding on my side. I thought he was asking for the algorithm of Fractint's Ljapunows. ;-) ...but together with the description one probably better understands, what's going on in the formula-file ... sorry again ;*) -- Michael LDKnet / LDK/LUG / Unix-AG *Weitzel* /LinuX --- email: michael(at)ldknet.org Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Gerald K. Dobiasovsky" Subject: Re: (fractint) Fractint Development: The Ljapunow Type Date: 03 Apr 2001 22:29:41 +0200 Michael Weitzel wrote: > sorry ... probably a misunderstanding on my side. I thought he was > asking for the algorithm of Fractint's Ljapunows. ;-) > > ...but together with the description one probably better understands, what's > going on in the formula-file ... sorry again ;*) No reasons to apologize... 1) Your explanation is a detailed and illuminating one. 2) Maybe I am wrong and he *was* asking for the algorithm?! Greetings, Gerald Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) Fractint Development: The Ljapunow Type Date: 03 Apr 2001 16:28:25 -0500 Michael Weitzel wrote: > > sorry ... probably a misunderstanding on my side. > I thought he was asking for the algorithm of > Fractint's Ljapunows. ;-) > I personally found your postings on the topic quite interesting, whether or not the original questions was for FRMs/PARs. It is always nice to have an understanding of the details. Thanks for sharing with all of us on the List. Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: (fractint) A Fractal Project Completed !! Date: 03 Apr 2001 16:55:14 -0500 Greetings, Philip Northover, the fractal artist known for his "Fractal Alhambra" website at: http://pnorthov.future.easyspace.com/ has recently completed a very lengthy project. Though Philip has five online galleries containing over a hundred images, he has also been working on his private project for approximately two years: "A Fractal Interpretation of the King James Version of the Bible" He kept to a classical fractal style throughout, employing the primary colours, which he fealt conveyed the biblical simplicity which often hints at great depths. Philip wanted an overall feeling of consistency, unity, order, and purpose to the work, while still reflecting the essence of each book within the Bible. I hope everyone has an opportunity to visit his web site to view what definitely has been a considerable personal project for Philip. Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Guy Marson Subject: Re: (fractint) Fractint Development: The Ljapunow Type Date: 04 Apr 2001 01:21:44 +0200 Hi, At 12:47 03/04/01 +0200, you wrote: >Am Montag, den 02. April 2001, um 00:11h schrieb Gerald K. Dobiasovsky: > >> > Does somebody know the Lyapunow-formula written for the Parser similar to >> > the build-in type, or a place (url or so) to find this formula? >[your frm + par files] > >sorry ... probably a misunderstanding on my side. I thought he was >asking for the algorithm of Fractint's Ljapunows. ;-) > It's ok, not being a math, now I understand the Lyapunow-type mutch better! Having both, the formula and more explanations Thanks to both of you! >...but together with the description one probably better understands, what's >going on in the formula-file ... sorry again ;*) nix zu entschuldigen, das ist voll in Ordnung so! >-- > Michael LDKnet / LDK/LUG / Unix-AG > *Weitzel* /LinuX --- email: michael(at)ldknet.org > cheers, Guy Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 04-04-01 (A New Midget [6]) Date: 03 Apr 2001 22:49:09 EDT Classic FOTD -- April 04, 2001 (Rating 6) Fractal visionaries and enthusiasts: I named today's not quite overwhelming fractal "A New Midget". And it's true -- this particular midget has never before been seen by the eyes of man, nor by the eyes of woman, who sometimes can see more than man. Of course, we always suspected that the midget existed. We know that an infinity of midgets exist, of which exactly zero percent, or more precisely an infinitesimal percent, will ever be seen. That's one of the curious things about midgets -- an infinity of them exist -- and regardless of how many we discover, the number of undiscovered midgets is never reduced. Take for example the parent fractal of today's midget. The default appearance is a drab set of concentric circles, with a twisted midget near the right edge of the screen. A couple out-zooms will reveal that the entire fractal appears as a roughly diamond-shaped island in the middle of an infinite ocean. The default midget is seen to be a lake on an island. This midget has some unusual things happening in its East Valley area, and today's scene lies deep in this East Valley area. Undecided how to rate today's effort, I finally decided on a slightly above average 6, making the image worth the effort of downloading it from paul's web site at: Unfortunately, Scott's FOTD site will be down for a few days. The fractal weather today was unexpectedly sunny and warm. Until the middle of the afternoon, the weather experts were forecasting that chilly clouds and rain would prevail all day. This caused them to appear a little less than expert, though the fractal cats had no complaints as they enjoyed the temperature of 61F (16C). And after another busy and confusing day, I will now enjoy an hour or so of relaxation. I'll return tomorrow around this same time with another moderately glorious fractal and a few words about the image. Until then, take care, and wait with bated, but not abated, breath. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_New_Midget { ; time=0:25:51.10--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.57276058003352300/+0.186020729751933\ 60/9.061857e+012/1.0002/-154.909/-0.094 params=-1/-1.5/100/5/-0.93/0 float=y maxiter=3000 inside=0 periodicity=10 colors=000td_sfbrheqjhplkonnnpqmrtjprhopenocmmallZ\ kjXjiUigShfQgdNfcLeaId`GcZEbYFcUGcRHcNHcKIdHJdDKdA\ Kd7LcAMbDNaGN`IO_LPZOQYRQYT_cbihlsmupipnfllchj`dgX\ _eUWcRSaOOZKJXHFVEBTB7R83TA5VC7XE8ZGA`ICbKDdMFfNGh\ PIjRKlTLnVNpXPrZQt`SuaTt_TtYTtWTtUTtSTsRTsPTsNTsLT\ sJTsIToDWk8Zh3akHdmLfpOirOkqQjqVjpVipVioUhoUhnUgnU\ gmTfmTflTelTeeXg__hUciOfjIjkCml6qm0tn3uk5uh8ufAucC\ uaFrZHoXJlUMiSOfQQcSS`UUYWWVYXS_VPaTMcRJeTJ`VKWXKR\ YKM_ONaSNcWOd_OfcPhgPikPZnUOqZEtcJjdOaeTSeYJfaAf`B\ g`Bg`Bg`Ch`Ch`Ch`Di_Di_Di_Ej_Ej_Ej_Fk_Fk_FkZJgYMcX\ P`XSXWVUVYQUaMUdJTgFSjCRm8Rp5Xf7aY9fOBkFDlEGmDInCL\ oBNpBQqASr9Vr8Xs7_t7au6dv5fw4ix3kx3ms8nnCnjHneLoaP\ oXUoTYpObpKfpFjqBoq6sq2wqAniIebQXWYOPeFIcLKbQMaVO`\ _QZeSYjUXoWWtYI`I5H35E37H68J99MCAOFBQICTLDVOEXRG_U\ HaXId_JfbKheLkhMmkNonPloQjpSgqTeqVcrW`sYZsZWt`UuaS\ ucPvdNweLwaMvrZPwYQv`UubX } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Spatzy2325@aol.com Subject: Re: (fractint) A Fractal Project Completed !! Date: 03 Apr 2001 23:42:13 EDT Good Evening, I am quite confused about the project... are these fractals represent the books of the Bible, or are the words themselves used in some way or form to create the fractals? Please respond as soon as possible, thanks, God Bless Ryan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "David Jones" Subject: (fractint) [fractal-art] Some links to fractal sites Date: 03 Apr 2001 18:07:08 -1000 Found these at Netscape's Open Directory Project: http://dmoz.org/Science/Math/Chaos_and_Fractals/ http://www.3dfractals.com/tetrapics/imageframe.htm David gnome@hawaii.rr.com _______ ______ _____ ____ ___ __ _ post: send message to fractal-art@lists.fractalus.com unsub: send message to fractal-art-unsubscribe@lists.fractalus.com help: send message to fractal-art-help@lists.fractalus.com admin: send message to fractal-art-owner@lists.fractalus.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "David Jones" Subject: (fractint) Some links to fractal sites Date: 03 Apr 2001 18:07:08 -1000 Found these at Netscape's Open Directory Project: http://dmoz.org/Science/Math/Chaos_and_Fractals/ http://www.3dfractals.com/tetrapics/imageframe.htm David gnome@hawaii.rr.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Programmer Dude Subject: Re: (fractint) Fractint Development Date: 04 Apr 2001 10:58:32 -0500 No one has responded to this in a couple days, so I thought I'd take a shot at it... Andrew Coppin wrote: >> The memory limitations stem from two sources. One is that Fractint is >> compiled in the medium memory model. This means that memory usable for >> near data is limited to 64KB unless some form of swapping is done. > > So, you mean that FractInt can as such only use 64KB of memory? Sort of. FractInt was born as an MS-DOS program, and MS-DOS ran on Intel chips. Intel chips see memory as "segmented" rather than "flat" (as the Motorola chips (used in Apple machines) do). Flat memory looks like one huge "address space". For any memory location from 0000000 to umpteenzillion, the memory location just refers to the appropriate point, like milage along a road. In segmented memory, a memory location consists of two numbers: a segment and an offset. The segment is like a rolling window that jumps in, IIRC, 256-byte jumps: segment 0 starts at 0, segment 1 starts at 256, and so on. And a segment is a 64-k "window". The offset refers to any location within that 64-k window. The Intel chips ran programs in an architecture that had four segments: a "Code" segment, a "Data" segment, a "Stack" segment and an "Extra" segment sometimes used as a second, extended Data segment). Due to the nature of the C language (a primary development language of the day), the Stack and Data segments usually had to be identical. You ended up with a 64-K window with your data growing from the bottom upwards and your stack growing from the top downwards. The space in the middle was the "heap" and is where you got dynamically allocated memory from. The "Memory Model" is what various configurations of the segments is called. Remember the old .COM programs? By definition, they always use the "Tiny" memory model. All segments are identical, and your entire program--data and code--must fit in a single 64-K window. The "Medium" memory model, IIRC, has the stack and data sharing one 64-K segment, while the code lives in its own 64-K segment. This doesn't mean the program can't access data outside these segments. It can, but outside memory is "far" in the language of Intel memory models (opposed to the "near" memory in the data/stack segment). Because the data/stack segment is "framed" by the segment pointers of the Intel architecture, you only need 16 bits (64-K) to address it. But since "far" memory is 'somewhere in address space' you need a full address which was, at the time, 24 bits usually expressed as two 16-bit values with 8 bits of overlap. Added together, they form a 24-bit address. The bottom line is that, in your program, you have a mix of "near" data and "far" data, and they require different variable types to refer to. > What's involved in such a change? Is it just a case of going through the > program and changing half a million lines of code on a find-and-replace > basis, or does it require an actaul redesign of the code? I can't speak for the FractInt developers, and I'm not familiar with the code. I can guess it lies between those two ideas. It's not a simple matter of S&R; I'd guess you want to examine every place you need to change to see if the change breaks anything. But it probably does NOT require a complete redesign. Ideally you'd like a compiler that let you treat memory as flat and make all your pointers be the same type. I have no idea if such exists for the Intel platforms. But then *I* think what you *really* want is to get away from MS-DOS. > I'd really prefer FractInt to remain a DOS program, or perhaps to have > a DOS *and* a Windows version. (...and a Linux/UNIX version, like they > do with POV-Ray. Hey... isn't that a Stone Soup project too?) Don't *think* POV-Ray (great program, BTW) is Stone Soup. There's actually a great concept there. POV-Ray renders to a disk file normally. The Windows version just happens to have the extra treat of showing you the image as it's rendered. But the heart of POV-Ray is a command line tool for rendering 3D scenes into an image file of some type. >> The other problem is that we do indeed use extended and/or expanded >> memory for options other than just disk video. Saving the on screen >> image when switching to a menu comes to mind. > > If you had more memory to play with, could this be avoided? (I understand > that disk video can use insane quantities of RAM, but keeping a copy of > the video buffer for a normal screen shouldn't be too bad...) But what I imagine they have to save is the fractal image while the menu screens are displayed. That could be considerable. Anyway, hope this little data dump helped rather than confused... -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Zorba the Hutt" Subject: Re: (fractint) Fractint Development Date: 04 Apr 2001 17:41:53 -0400 > > Ideally you'd like a compiler that let you treat memory as flat and make > all your pointers be the same type. I have no idea if such exists for > the Intel platforms. > > But then *I* think what you *really* want is to get away from MS-DOS. > Any 32-bit compiler does this - basically, anything that compiles native Win95 programs or higher. There *is* a way to use flat memory on MS-DOS, as I remember - the DOS4GW extension, that everyone who's played games in the late DOS era will recognize. It was basically a protected-mode flat memory manager, and you needed a 32-bit compiler to use it, and by golly, it was worth it. At least, I think that's what it did. Correct me if I'm wrong ^^;; -Zorba Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Multiple Bogeys" Subject: Re: (fractint) FOTD 03-04-01 (Many Happy Returns [5]) Date: 05 Apr 2001 01:24:33 -0400 ------=_NextPart_001_0000_01C0BD6F.2B90BFE0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > Today, the FOTD returns after its 1-1/2 week hiatus, with the > first fractal I've calculated in that time. Of course, this is > the reason I have named it "Many Happy Returns. The average > rating of 5 reflects my opinion of my first fractal effort in > 11 days. ^ Error: Unterminated string constant. :-) > Unfortunately, I still lack the time for the long philosophical > discussions that have made the FOTD what it is :-/ but as > things gradually return to normal in the near future, the FOTD > discussions will become longer and more complex, until hopefully > we finally solve the mystery of the universe. :-\ Hate to tell you this, but it's already been done. http://www.hep.upenn.edu/~max/toe.html
Get Your Privat= e, Free E-mail from MSN Hotmail at htt= p://www.hotmail.com.

------=_NextPart_001_0000_01C0BD6F.2B90BFE0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
> Today, th= e FOTD returns after its 1-1/2 week hiatus, with the
> first fracta= l I've calculated in that time.  Of course, this is
> the reas= on I have named it "Many Happy Returns.  The average
> rating = of 5 reflects my opinion of my first fractal effort in
> 11 days.            = ;  ^
Error: Unterminated string constant. :-)
=
> Unfortunately, I still lack the time for the long philosophical<= BR>> discussions that have made the FOTD what it is  :-/  bu= t as
> things gradually return to normal in the near future, the FO= TD
> discussions will become longer and more complex, until hopeful= ly
> we finally solve the mystery of the universe.  :-\
Hate to tell you this, but it's already been done.
http://www.hep.upenn.edu= /~max/toe.html

 


Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

------=_NextPart_001_0000_01C0BD6F.2B90BFE0-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Multiple Bogeys" Subject: Re: (fractint) Fractint Development Date: 05 Apr 2001 01:37:30 -0400 ------=_NextPart_001_0001_01C0BD70.FB2274A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable You can also use djgpp and cwsdpmi to get 32-bit flat memory programs for= MS-DOS. If you use Allegro as an API to mouse/low-level keyboard/graphic= s/etc. stuff, as an added bonus it is easily ported to Windows and Linux,= since Allegro has been ported to these and gcc (of which djgpp is a port= ) exists for Linux and has at least 2 Windows ports.
G= et Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

------=_NextPart_001_0001_01C0BD70.FB2274A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
You can also u= se djgpp and cwsdpmi to get 32-bit flat memory programs for MS-DOS. If yo= u use Allegro as an API to mouse/low-level keyboard/graphics/etc. stuff, = as an added bonus it is easily ported to Windows and Linux, since Allegro= has been ported to these and gcc (of which djgpp is a port) exists for L= inux and has at least 2 Windows ports.


Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

------=_NextPart_001_0001_01C0BD70.FB2274A0-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) Re: FOTD 03-04-01 (Many Happy Returns [5]) Date: 05 Apr 2001 07:25:18 EDT I wrote: >> .....the FOTD discussions will become >>longer and more complex, until hopefully we finally solve the >>mystery of the universe. :-\ Multiple Bogeys replied: >Hate to tell you this, but it's already been done. Aw shucks, I missed it! ;-( FOTD in one hour. Jim M. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 05-04-01 (Specular Reflection [6]) Date: 05 Apr 2001 08:31:11 -0400 (EDT) Classic FOTD -- April 05, 2001 (Rating 6) Fractal visionaries and enthusiasts: Once again, due to unavoidable things that had to be done, the FOTD is late. This will continue to happen occasionally until things are totally back into the familiar routine here at the new Fractal Central auxiliary. Despite the rush, I managed to find a fractal midget worthy of a rating of 6. I named the picture "Specular Reflection" when I had the impression of a brilliant light reflecting from a metallic surface around the edges of the midget. The formula behind the image is another of my whimsical ones -- -(Z^(-1.25))+Z^(1.25)+(1/C). The 6-1/2 minute render time of the parameter file is just slow enough to make a download of the GIF image worth the effort. That image will soon be available on Paul's web site at: Scott once again has his site up and running. The GIF image will also soon be available there at: The fractal weather today was sunny and mild, with a temperature of 59F (15C), which the fractal cats found ideal. They spent nearly the entire afternoon sunning themselves in the yard and thinking of what trouble to get into. I lack the time today to reveal the one true mystery of the universe, but I must warn about all those false mysteries of the universe out there. Don't be deceived by these imitations, wait for the real thing to be revealed. ;-) Until the real thing is revealed, and even after the revelation, I'll continue with the 4-year-old FOTD, which has no end in sight. The next one will appear in about 15 hours. I'll see you then. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ SpecularReflection { ; time=0:06:30.52--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.466396676467665/+1.55164254988776/1.\ 393514e+012/1/-50.009/0.012 params=-1/-1.25/1/1.25\ /0/0 float=y maxiter=1400 inside=0 logmap=125 periodicity=10 colors=000B8ZB7`C6cD5fE3iF3lG2oH1pE0oC2mB3jA5f87c7\ 8_6AW5BT9DUCHXHKYKN`RRaYYdddfiiinnnssswwwzzzzzzzzz\ tttlllddiYYhRRdKKcEE`98ZE3XK1WR5TY9QdDPlIMtNKzTIzY\ HzZGz`Ez`EzaDzaCzcCzcBzdAzdAzf9zf9zhAyiAtiAokAnlAk\ lAhnAdoBaoB`qBYsBWsBTtBQuBPuBToDWiEYcG`YHcTIfPJiJM\ lENoAPs6Qu2Ry0T1d03`17X39U5CQ7EM9IJBMGEPCHTAJW7MZ3\ Pa2RotPosNnqMnoKnoJlnIllH1oR0oR0oQ0oQ0oP0oP0oN0oN0\ oN0nM0nK0lK0lJ1lI2lI3kI3kH5iH6iG8iE9hEAhDBfDCfCEfB\ GdBHdAIcAKc9Mc8Na8Pa7Q`7T`6U`5WZ5XZ3YY3`Y3aY2cX2dX\ 10U60U50U51U52U53U53U55U56U57U38U38U39U3AU3BU3CU3D\ U3EU3GU3HU3IU3IU3JU3KU3MU3NU2PU2QU2RU2TU2UU2UU2WU2\ XU1YU1ZU1`U1aU1cU1dW1fX1j`NqZInYDhYUhZck`miawiczid\ sifnihihidhk`hlXhnThoPhqKfsHftDfuAfw7fy39z0Gz0Mz0T\ z0Zz0RzPTzNTzNTzMTzMUzKUzKUzJUzJWzIWzIWzHWzHXzHXzG\ XzGXzEYzEYzDYzDYzCZzCZzBZzBZzBZzA`zA`z9`z9`z8az8az\ 7az7az6cz6cz6cz5cz5dz3dz3 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 06-04-01 (Rainy Evening [6]) Date: 05 Apr 2001 20:29:11 -0400 (EDT) Classic FOTD -- April 06, 2001 (Rating 6) Fractal visionaries and enthusiasts: Things were really hopping today here at Fractal Central II. My efficiency was at its maximum however, and I finished the day's jobs in near record time. This burst of efficiency gave me more time than expected to search the world of numbers for a fractal worthy of being christened FOTD for April 6. The world I chose to search is the one created by the whimsical formula 0.3(Z^2)-7.5(Z^(-0.1))+(1/C). I was not disappointed with what I found there. Today's fractal is named "Rainy Evening", a name that was inspired by the cusps surrounding the midget, which remind me of the pattern seen around street lights when viewed in the evening through water droplets on one's eyeglasses. After some indecision, I rated the picture, which is just slightly above average, at a 6. A year or two ago I might have rated it a 7 or 8, but my opinion of what constitutes an 'average' FOTD image seems to be growing ever more strict, and if the present trend continues, I'll have a hard time producing even an average FOTD. The parent fractal of today's image is a grossly mis-shapen Mandeloid, so twisted and torn that it is barely recognizable. At the southwest corner of the figure lies a Mandel-bud with a filament that extends in a disjointed manner into the Seahorse Valley area of a satellite midget. Since filaments usually join midgets in the East Valley area, this unusual junction appeared a likely place to start the day's search. The result speaks for itself, figuratively speaking of course. The result of all this effort may be seen by running the attached parameter file and waiting 5 minutes, or by giving Paul and Scott a chance to post the GIF file of the image to their web sites, and downloading it from there. The URL of Paul's web site is: And Scott's is: The weather today turned out to be the finest of the young Spring season, with bright sun, light winds, and a temperature of 64F (18C), which kept the fractal cats outdoors for several happy hours. The fine weather also stirred my philosophical muse, once again raising unanswerable questions about the nature of reality. Every time I discuss this tired, worn-out, but ever-fascinating topic I seem to get into trouble. So stay in touch. I might be in more trouble in a few days' time. But for now it's time to shutter down the fractal shoppe and call it an evening. . . . OK, so it's an evening! Until next time, take care, and the more one wonders about what's real, the less one knows for sure. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Rainy_Evening { ; time=0:05:15.04--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.12191239695861750/-0.037765464265300\ 23/3.704671e+008/1/30 params=1/2/-25/-0.1/-0.7/0 float=y maxiter=1200 inside=0 logmap=91 periodicity=10 colors=000000G1AJ1JQ1SV3a`3je3ql3zxIpzXdvYllYr`_xQ\ _zF`z4`z6Vz7Pz9JxADrA9mDAoFApICrJCsMDuODvQFxSFyQDv\ QCsQApPAoP9lP7iO6fO6dO4aM3_M1XM1VL9YLF_LL`LScLYdJc\ fJjiJpjJvlJzm0Tz0Pz3Mz9IzGFzOAxT7v`4sg0pm0ou0lz0iz\ 0g0zT0zI9z77v66s66o64l44g43d41a31Y30V30Q10O10L10L0\ 0J00J0P66P9CQCGQFMQIQSLXSO`SQdTTjTXoT_uVayVdzVgzVj\ z_lzamzdmvgopjpjmpdpr_ssTvsOyuIzvCzv6zx0zy0zy0zz0x\ z0pz4iz9`zFTzJMzOFzS7zX6z`4yd4si3lm1fr1_v0Tz0Mz0Gz\ FYpVmYizFfzGczG`zGYzGVzGSzGPzIMzIJzIGzIDzICzIFzGIv\ GLsGOoGQlGTgGXdG_`GaYGdTGgQGjMGmJGpFGrCGoAJm9Mj7Pi\ 6Sf4Td3Xa1_`0aY0dX0fV1cT4aS7`SA_QDYPGVOJTOLSMOQLQP\ JTMJXLI_JGaIFdGFfF4pP0z_0zi0zg0zf4zdAzcFzcLzaQz`Xz\ _azYfzYczX`zXYzXVzXSzXPzVMzVJzVGzVDzVAzVDzSGzQJzOM\ zMPzJSzIVzFYzD`zCcz9fz7iz4lz3oz0rz0uz0czXfzOizGlz7\ oz0lz0jz0iz0gz0fz0dz0cz0az0`z0_z0Yz0Xz0zz0yz0vz0sz\ 0pz0mz0iz0dz0az0Yz0GzADz4 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Multiple Bogeys" Subject: (fractint) Oh no! Something is *very* wrong with the FOTD! Date: 05 Apr 2001 22:43:55 -0400 ------=_NextPart_001_0001_01C0BE21.E5AD1E20 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable ...the last four have all been grossly underrated. ;-) Keep up the good w= ork!
Get Your Private, Free E-mail from MSN Hotmail at= http://www.hotmail.com.

------=_NextPart_001_0001_01C0BE21.E5AD1E20 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
...the last fo= ur have all been grossly underrated. ;-) Keep up the good work!


Get Your Private, Free E-mail from= MSN Hotmail at http://www.hotmail.com= .

------=_NextPart_001_0001_01C0BE21.E5AD1E20-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) C-FOTD 06-04-01 (Rainy Evening [6]) Date: 06 Apr 2001 10:07:07 -0500 Jim Muth wrote: >> At the southwest corner of the figure lies a Mandel-bud with a filamen= t that extends in a disjointed manner into the Seahorse Valley area of a satellite midget. Since filaments usually join midgets in the East Valle= y area, this unusual junction ... << Very unusual indeed!!! I don't think I've ever seen such a junction! Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 07-04-01 {Fractal Dimples [6]) Date: 06 Apr 2001 22:49:09 EDT Classic FOTD -- April 07, 2001 (Rating 6) Fractal visionaries and enthusiasts: Another unexpectedly busy day kept the fractals at bay, but I still managed to scrounge up today's slightly striking image. I first found it, then went off to do other things while the image rendered. When I returned and saw the screen, I thought of dimples. The name "Fractal Dimples" came naturally. The image is yet another 6-rated one found in haste. Unfortunately, the haste vanishes when the parameter file starts running, since this one takes over 1-1/2 hours to render. The formula that drew the image, 0.5(Z^2)+Z^(-2)+(1/C), is once again one that I pecked out at random. Since the parameter file is quite slow, my advice is to give Paul and Scott an hour or so to render and post the GIF image to their Web sites, and download it from there. The URL of Paul's site is: Scott's site is at: The fractal weather today was mostly cloudy with light rain and a temperature of 55F (13C). The cats disapproved vigorously by staying indoors and sulking most of the afternoon. There was no time for philosophy today. Perhaps it will appear tomorrow. But even if the philosophy is absent, a new and unique fractal will appear in the next FOTD. Until then, take care, and wait until you see that fractal! Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fractal_Dimples { ; time=1:33:02.89--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-13.91207242091377000/+18.4986369015475\ 7000/11315.38/1/165 params=0.5/2/1/-2/0/0 float=y maxiter=25000 inside=0 logmap=420 periodicity=0 colors=000e8me7me7mf7nf7nf6nf6of6of6og4nf5of6of7of\ 8of9ofAofBofCoeDpeEpeFpeGpeHpeIpeJpeKpdLqdMqdNqdOq\ dPqdQqdRqdSqcTrcUrcVrcWrcXrcYrcZrc_rb`sbasbbsbcsbd\ sbesbfsbgsahtaitajtaktaltamtantaou`pv`qv`rv`sv`tw`\ uw`vw`wxayy`xz`wz`wz_vz_uy_uxZtwZsuZssYrqYqoYqlXpk\ XpjXoiWniWnhWmgVlfVleVkdUjcUjcUibThaTh`Tg_TgZSfYSe\ XSeXRdWRcVRcUQbTQaSQaRP`RP_QP_POZOOZNOYMNXLNXKNWKM\ VJMVIMUHLTGLTFLSELSEKUFJVFIXFHYFGZFF`FFaFEbFDdFCeF\ BfGAhG9iG9jG8lG7mG6nG5pG4qG3sF4rG5qG6pG7oG7nG8mG9l\ GAkGAjGBiGChGDgGDfGEeGFdGGcGHbGHaGI`GJ_GKZGKYGLXGM\ WGNUGNSGQQGSOGUNGUMGULGUKJUHIUDIU6IU3HU3HU3HU3HU3G\ U3GU3GU3GU3FU3FU3FU3FU3EU3EU3EU3EV3DW3DX3DY3DZ3C_3\ C`3Ca3Cb3Bc3Bd3Be3Bf3Ag3Ah3Ai3Aj59k59l59m37n48o59p\ 5Aq6Br5Cs5Ct6Du6Ev7Fw8Gx8Hy9HzDIzEJzFKzFLzGMzGMzHN\ zIOzJPzKQzKRzLRzMSzMTzNUzNVzOWzPWzPXzQYzQZzR_zT`zV\ azXbzZcz`ezbfzdgzfhzhizjj } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: jerome schatten Subject: Re: (fractint) C-FOTD 07-04-01 {Fractal Dimples [6]) Date: 07 Apr 2001 23:20:01 -0700 JimMuth@aol.com wrote: [...] . When I returned and saw the screen, I thought > of dimples. The name "Fractal Dimples" came naturally. > A beauty... but perhaps "Fractal Pimples" ? jerome Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 08-04-01 (A Midget Eruption [6]) Date: 08 Apr 2001 07:55:48 EDT Classic FOTD -- April 08, 2001 (Rating 6) Fractal visionaries and enthusiasts: Yes, yes, I realize that the FOTD is once again late. It's late because I spent most of my spare time today organizing the new Fractal Central auxiliary HQ, leaving me little time for fun with fractals. But by entering values at random and searching aimlessly, I managed to find a fractal worthy of being declared today's FOTD. I named the fractal image "A Midget Eruption". The reason is most likely that I was impressed by the eruption of unusual features in the elements surrounding the ever-present midget at the center. The overall pattern resembles the typical Julia pattern that characterizes midgets found in the East Valley area of larger midgets, but today's midget has far more intricate detail than most. I have rated the picture a 6, the fourth or fifth 6 rating in a row. It's really quite an interesting scene. Maybe if I had more time to appreciate it, I would have rated it higher. The parameter file renders in under 9 minutes, slow enough to make a download of the GIF image worth the effort. That image will be available in an hour or so at: and at: The fractal weather today was unpleasant -- cloudy and chilly, with just enough light rain to keep the fractal cats confined to the indoors. Afternoon temperatures in the 50's F (lower teens Celsius) did not help. And now it's late, or more accurately, early, and I've got a lot of organizing to do. So until the next FOTD, take care, and all rushes eventually come to an end. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Midget_Eruption { ; time=0:08:46.12--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.127297927751329/-0.054242224379125/1\ .173881e+007/1/167.499 params=1/1.9/-25/-0.1/-0.7/0 float=y maxiter=1500 inside=0 logmap=156 periodicity=10 colors=000VM_XL_ZN`aQ`cU`eY`h``jcalfaojaqnasramiYh\ aVcUSYLOTDLO5INFOMPTLPZLPWJPTHSIGQJGOKGMLFLMFJNFHO\ EGPEEQECRDBSD9TD7UC6VC4WC2XC1YH3VL5SP6PT8MXAJ`BGdD\ DhFAlG7pI4tJ1qU3nc4lm5`oJPpWDri1sv1mq1gm1bi1Xe1SaG\ NTUIKhDBv82105EAEQJMbSVn`bzijsVfmHbg3Ze9ZdFZbKZaQZ\ _VZZ`ZXeZWkZVpZYiX_cVaYUcRSeLQgFPeGOdHNcIMbJLaKK`L\ J_MIZNHYOGXPFWQEVRDUSCTTCRUIQUNPUSNUYMUbLUgJUmIUrH\ UwMSsRRpVQm_PidOfhNcPbBScCUcDXdDZdE`eFceFefGgfGjfH\ lgIogIqhJshKviKxiLziLxyTtvUqsUnpVknVhkWehWbeX_cXW`\ YTYYQVZNTZKQ_HN_EK`BI`AH_9HZ8HZ8HY7HY6HX5HW5HW4HV3\ HV2HU2HU5GS8GQBGPEGNHGLKFKNFIQFHTFFWFDZECaEAdE8gE7\ jE5mE4jF6gG8eG9bHB`ICYIEWJFTKHRKIQMJQOJPPJPRJOTKOU\ KOWKNYKNZLM`LMbLMcLJZNHVPFQRDMTBIVAOZ9Ta9YdBZbC_aD\ ``E`_FaZGbYHbXKcYMcZOcZRd_Td_Vd`Yea_eaaebdfbfgchhd\ kidmjeokeplaqmZrmWsmStmPumMvmIwmFwmCwm8wm5wm2wm6wm\ AwmEwmIwmMwmPwmTwmXwm`wmd } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 09-04-01 (Mandelbrot Mayhem [5]) Date: 09 Apr 2001 00:42:15 -0400 (EDT) Classic FOTD -- April 09, 2001 (Rating 5) Fractal visionaries and enthusiasts: With today's 5-rated fractal image we break away from the string of FOTD's that have been rated a 6. Unfortunately, the break is in the less desirable direction, but then one can't have everything. We also break away from the world of the MandelbrotMix4 formula into the world of the MandelbrotBC formula to explore the more remote parts of the fractal created by the very simple formula, Z^(sqrt2)+C. The scene I found is one of the most disorderly of all time, with bits and pieces of fractal stuff scattered around the midget in total disarray, showing no signs at all of an orderly arrangement. The unusually chaotic image is well worth the name I gave it -- "Mandelbrot Mayhem". At just under 13 minutes, the parameter file tries one's patience. Relief for the impatient is available on the Web at: and at: where the GIF file of the image will soon be posted. The fractal weather today started cloudy and chilly, but turned sunny and milder at midday. The bright sun and afternoon temperature of 63F (17C) then lured the fractal cats into the yard, where they sampled the new grass. It's now time to shut down the shoppe and call it a night. Until tomorrow around this same time, take care, and one of these days someone will find the ultimate fractal -- but will they recognize it?. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Mayhem { ; time=0:12:54.45--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotBC passes=1 center-mag=+0.45672737879421720/+0.492387056367433\ 40/1550.388/1/92.5 params=1.414213562373/0/11/0 float=y maxiter=6000 inside=0 logmap=128 symmetry=none periodicity=10 colors=000W`eYei`jmbnqidizMauMUpNQlNMgOJcOF_OCZNDY\ MDXLDWKDWJDVIDUHETGETFESEERDEQCEQBERAIR9LS9OS8RS8U\ T7XT7_T6bU6eU5hU5kS9lRCmPFnOIoMMpLPpJSqIVrGZsFatDd\ uCguQaacXJpS0mQ3jP6gO9dNBaMEZLHXKJUJMRIPOHRLGUIFXG\ EZKG`NIbQJdULfXNh_OjbQlfSniTplVroWtnXomXklYgkYcjY_\ iZWiZShZOg_Kf_Ge_Cd`8c`4c`0fbAhdKjfTfKsiNlkQfnS_pV\ UrYNu_HwbAyd4w_5uV5sR5qM5oI5mK9kLDiMHgNKbLIZKGVJEQ\ ICMGAIF8DE69D45C26D56E86EA7FD7GF7GI7HK8IN8IP8JS8JU\ 9KV9KVALVALVAMVBMWBNWCNWCOWCOWHTZLY`PbbTfdRegPdjNc\ mLcpJbsHavFaxHgoJmfKsYGj_Db`AVd7Mg4Ei16k28l2Am2Cn2\ Eo2Gp2Iq2Kr2Ms2Ot2Qu3Sv4Uw5Ww5Yw6_w7aw8cw8ew9gwAiw\ BkwBmwCovDpuDqtErsErrFpqFnoFmoGknGjoGipHiqHirHirIi\ qIiqIiqIiqIiqIiqIiqNjqIiqIiqJiqJiqJiqJiqJiqJipJipJ\ ipJipKipKipKipKipKipKipKipKipKipKipLjoLjoLjoLjoLjo\ LjoLjoLjoLjoMjoMjoMjoMjoMjoMjnMjnMjnMjnNjnNjnNjnNj\ nNjnNjnNjnNjnNjnCilDjmDjm } frm:MandelbrotBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Programmer Dude Subject: Re: (fractint) C-FOTD 09-04-01 (Mandelbrot Mayhem [5]) Date: 09 Apr 2001 10:38:14 -0500 Jim Muth wrote: > ...and one of these days someone will find the ultimate fractal -- but > will they recognize it?. Why should there *be* an ultimate fractal? Seems kind of limiting... -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 10-04-01 (A Naming Problem [4]) Date: 10 Apr 2001 07:58:03 EDT Classic FOTD -- April 10, 2001 (Rating 4) Fractal visionaries and enthusiasts: Another very busy day at Fractal Central left insufficient time for a proper fractal search, so I turned to a strange image I found a week or so ago. Being only a backup, the image comes down another notch on my scale of fractal worth, rating only a 4 on the scale. I named the picture "A Naming Problem" because of the complexity of the Mandeloid that fills the frame. It's hard enough to identify the various features of the classic Mandelbrot set by colloquial names. Imagine the problem if such a naming system were applied to the many parts of the Mandel- thing in today's image. To make matters even more difficult, the image has a strange kind of symmetry. The Y-axis symmetry of the Mandel-shaped feature is obvious, but there are bits of foreground debris scattered throughout the picture, which have no symmetry whatsoever. I suspect that this unusual symmetrical- unsymmetrical character is caused by the two different exponents of the formula, one of which is positive, the other negative. But I'm not positive. Regardless, the parameter file renders in about 9 minutes, and the GIF file of the image will soon be available on the Web at: and at: The fractal weather today here at Fractal Central started with a light thunder-shower, turned unusually sunny and warm, then ended with a heavy thunder-storm. The fractal cats approved of the 90F (32C) temperature by basking all afternoon in the shade of the holly trees, but they disapproved of the noise of the evening storm. As for me -- I worked all day. And tomorrow will likely be just as busy, but I'll still manage to find at least one fractal. Until then, take care, and see you in 16 hours. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Naming_Problem { ; time=0:08:53.78--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=0.0881747/0.0124835/0.4235847/1/-90 params=-0.075/2/10/-2.25/-0.88/1000000000 float=y maxiter=3000 inside=0 logmap=7 periodicity=10 colors=000fQLeQLeQLeQMePMePMePMePMdPMdONdONdONdONd\ ONdNOcNOcNOcNOcMOcMOcMPcMPbMPbLPbLPbLPbLQbLQbKQaKQ\ aKQaKRaKRaJRaJRaJR`JR`IS`IS`IS`IS`IS`HT_HT_HT_HT_H\ T_GT_GU_GUZGUZGUZFUZFUZFVZFVZEVYEVYEVYEWYEWYDWYDWY\ DWXDWXDXXCXXCXXCXXCXWBWXCXXCXXCXXCXXDXXDXXDXXDXXDX\ XEXXEXXEXXEXXFYXFYXFYXFYXFYXGYXGYXGYXGYYGYYHYYHYYH\ YYHZYIZYIZYIZYIZYIZYJZYJZYJZYJZYJZYKZYKZYK_YK_YL_Y\ L_YL_ZL_ZL_ZM_ZM_ZM_ZM_ZN_ZN_ZN_ZN`ZN`ZO`ZO`ZO`ZO`\ ZO`ZP`ZP`ZP`ZP`ZQ`ZQ`_Qa_Qa_Qa_Ra_Ra_Ra_Ra_Ra_Sa_S\ a_Sa_Sa_Ta_Tb_Tb_Tb_Tb_Ub_Ub_Ub_Ub_Vb`Vb`Vb`Vb`Vb`\ Wc`Wc`Wc`Wc`Wc`Xc`Xc`Xc`Xc`Yc`Yc`Yc`Yc`Yc`Zd`Zd`Zd\ `ZdaZda_da_da_da_da`da`da`da`da`eaaeaaeaaeaaeabeab\ eabeabeabeaceaceacebcfbcfbdfbdfbdfbdfbefbefbefbefb\ efbffbffbfgbfgbfgbggbggbggbggbhgbhgchgchgchgcigcig\ cihcihcjhcjhcjhcjhcjhckhckhckhckhckhclhclicliclicm\ idmidmidmidmidnidnidnidni } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Guy Marson Subject: (fractint) a little tease Date: 11 Apr 2001 10:41:45 +0200 Hi Fractinters, 1) run this .par with its original values.. 2) reload the 'first1.gif' and set REAL(P4) to 35 .. (Z-screen) 3) set REAL(P5) to 0.1'500'000'002 (zero point 1500000002 :-) 4) now reload the 'second1.gif' and set REAL(P4) to 30 .. (Z-screen) 5) set REAL(P5) to 0.1500000001 .. If you wanna experiment with the text, set IMAG(P4) to e.g. 0.14 Thanks to Sylvie Gallet, Jim Muth and Jan Marten van der Walk for their fantastic pattern! ************************* par and frm's: ************************* first1 { ; Version 2001 Patchlevel 6 reset=2001 type=formula formulafile=lakerise.frm formulaname=lakerise function=recip/ident passes=1 center-mag=+19.06420449201231000/+0.00105725129748224/6.787838e+007/0.93\ 15/90 savename=first1 params=95158716/1/0.015/0.51/2.55e-009/-1.25e-008/85/0.15/0.15/1 float=y maxiter=6000 inside=0 logmap=46 periodicity=0 colors=00082A<3>819818818907<3>H46J46L55<2>T85V94YB4_C3bD3<3>lI2nJ1pK1rM\ 0<6>v`4vb5wd5wf6xi6<2>xm8xn9yn9<3>yrCysDytEyuE<17>zwczwdzwfzwh<3>zwmzvoz\ vpzvrzvszuu<104>P77P77P77<6>M33M33M22<3>K000CP<3>0BO0BO0BO<4>0AL0AL0AK<3\ >0AK0AK0AK<12>46G46G46F56F55F55F<3>64D64D74D<3>73D73C73C73B73A73A72A } second1 { ; Version 2001 Patchlevel 6 reset=2001 type=formula formulafile=e-viva-c.frm formulaname=e-viva-c function=recip/ident passes=1 savename=second1 center-mag=+19.06442878086688000/+0.00068889924650949/6.303265e+007/1/47\ .499 params=95180095/1/0.1/0.4/-2.56e-008/3.32e-008/90/0.15/0.15/1 float=y maxiter=6000 inside=0 logmap=55 periodicity=0 colors=00082A<3>819818818907<3>H36J46L55<5>_C3bD3eE3<3>nJ1pK1rM0<6>v`4vb\ 5wd5wf6xi6<2>xm8xn9yn9<3>yrCysDytEyuE<17>zwczwdzwfzwh<3>zwmzvozvpzvrzvsz\ uu<96>SAASAAR99<5>P77P77P77<4>N44N44M33<3>L11L11K000CP<3>0BO0BO0BO<4>0AL\ 0AL0AK<3>0AK0AK0AK<12>46G46G46F56F55F55F<3>64D64D74D<6>73C72B72B82A } frm:lakerise { ; lake-transformation = Sylvie Gallet, Jan 16, 2000 ; requires: float=on, Fractint 20.0.6, periodicity=0' and 'passes=1' ; real part of p1: diameter of text bailout ; imag part of p1: position of text bailout (x and y) ; real part of p2: merging of text (position) ; imag part of p2: merging of text (position) ; real part of p3: x-position of text bailout versus background ; imag part of p3: y-position of text bailout versus background ; real part of p4: 0 = lake transform disabled ; any value between 0 and 100: water level in % of ; the screen height (0 = bottom, 100 = top) ; Try fn1=recip, fn2=ident: If (A=B*C) then text=invisible, else=visible! ; imag part of p4: A (position of text & picture bailout) ; real part of p5: B (position of text bailout) ; imag part of p5: C (position of picture bailout) ; to position text into the picture, try e.g.: A=0.18, B=0.18005, C=1 ; finaly set B to the best value found by 'try and error' pp_p3 = (0.2,300) ; 0.2=amplitude and 300=frequency of the lake ; Lake transformation ; ------------------- if (real(p4) > 0 && real(p4) <= 100) level = real(p4) / 100 ; water level ampl = real(pp_p3) ; amplitude of the wave freq = imag(pp_p3) ; frequency angle = real(rotskew * pi / 180) exp_irot = exp(-flip(angle)) h = 1 / real(magxmag) w = h / 0.75 * imag(magxmag) tanskew = tan(imag(rotskew * pi / 180)) u = 2 * w * exp_irot v = 2 * h * (tanskew + flip(1)) * exp_irot z3rd = center + (-w-h*tanskew - flip(h)) * exp_irot z = pixel - z3rd b = imag(conj(u)*z) / imag(conj(u)*v) if (b <= level) dy = level - b z = z + 2*dy * (1+ampl*sin(freq*dy^0.2)) * v endif pixel = z + z3rd endif z=(sinh(sinh(sinh(pixel-p3)-real(p1))-p2))/imag(p1) x=real(z), y=imag(z) ;Text = generated with FRACTEXT.EXE from J.M.v.d. WALK chrI1 = x>-0.51186&&x<-0.49236 chrS2 = abs(cabs(z+(0.43498,-0.70762))-0.03262)<0.00975&&(x<=-0.434\ 98||y>0.70762)||(abs(cabs(z+(0.43498,-0.64238))-0.03262)<0.00975&&(\ x>-0.43498||y<0.64238)) chrF4 = x<-0.28311||(y<0.68475&&y>0.66525)||y>0.7305&&x>-0.30261&&x\ <-0.22311 xCR=2*x chrR5 = y<0.68475&&y>0.66525||y>0.7305||x<-0.18861&&x>-0.20811&&x<-\ 0.15861||(abs(cabs(z+(0.15861,-0.70762))-0.03262)<0.00975&&x>=-0.15\ 861)||(y<0.675&&y<-xCR+0.36753&&y>-xCR+0.32393) xCA=3*x chrA6 = y>xCA+0.84203||y>-xCA+0.5963||(y<0.66&&y>0.6405)&&yxCC+0.56568||y<-xCC+0.78432) chrT8 = y>0.7305&&x>0.17736&&x<0.27186||(x>0.21486&&x<0.23436) chrI9 = x>0.28686&&x<0.30636 xCN=2.5*x chrN10 = x>0.32136&&x<0.34086||(x>0.38136&&x<0.40236)||(y>-xCN+1.55\ 339&&y<-xCN+1.60589) chrT11 = y>0.7305&&x>0.41736&&x<0.51186||(x>0.45486&&x<0.47436) test1 = chrI1||chrS2||chrF4||chrR5||chrA6||chrC7||chrT8||chrI9||chr\ N10||chrT11&&y>0.6&&y<0.75 chrS12 = abs(cabs(z+(0.64457,-0.4936))-0.0286)<0.0078&&(x<=-0.64457\ ||y>0.4936)||(abs(cabs(z+(0.64457,-0.4364))-0.0286)<0.0078&&(x>-0.6\ 4457||y<0.4364)) chrI13 = x>-0.59517&&x<-0.57957 chrN14 = x>-0.56657&&x<-0.55097||(x>-0.51457&&x<-0.49776)||(y>-xCN-\ 0.88641&&y<-xCN-0.84441) xCK=1.5*x chrK15 = x<-0.46916||(yxCK+1.14236)||(y>-xCK-0.2404\ 8&&y<-xCK-0.21236&&y-0.48476 chrI16 = x>-0.39524&&x<-0.37964 chrN17 = x>-0.36664&&x<-0.35104||(x>-0.31464&&x<-0.29784)||(y>-xCN-\ 0.38659&&y<-xCN-0.34459) chrG18 = abs(cabs(z+(0.21984,-0.465))-0.0572)<0.0078&&(x<-0.21984||\ y<0.4728||y>0.4806)||(x>-0.21984&&x<=-0.17044&&y<0.4728&&y>0.4572) chrO20 = abs(cabs(z+(0.01184,-0.465))-0.0572)<0.0078 chrR21 = y<0.4728&&y>0.4572||y>0.5144||x<0.08176&&x>0.06616&&x<0.10\ 776||(abs(cabs(z+(-0.10776,-0.4936))-0.0286)<0.0078&&x>=0.10776)||(\ y<0.465&&y<-xCR+0.68833&&y>-xCR+0.65345) chrR23 = y<0.4728&&y>0.4572||y>0.5144||x<0.23776&&x>0.22216&&x<0.26\ 376||(abs(cabs(z+(-0.26376,-0.4936))-0.0286)<0.0078&&x>=0.26376)||(\ y<0.465&&y<-xCR+1.00033&&y>-xCR+0.96545) chrI24 = x>0.31316&&x<0.32876 chrS25 = abs(cabs(z+(-0.37816,-0.4936))-0.0286)<0.0078&&(x<=0.37816\ ||y>0.4936)||(abs(cabs(z+(-0.37816,-0.4364))-0.0286)<0.0078&&(x>0.3\ 7816||y<0.4364)) chrI26 = x>0.42756&&x<0.44316 chrN27 = x>0.45616&&x<0.47176||(x>0.50816&&x<0.52497)||(y>-xCN+1.67\ 041&&y<-xCN+1.71241) chrG28 = abs(cabs(z+(-0.60297,-0.465))-0.0572)<0.0078&&(x<0.60297||\ y<0.4728||y>0.4806)||(x>0.60297&&x<=0.65237&&y<0.4728&&y>0.4572) test2 = chrS12||chrI13||chrN14||chrK15||chrI16||chrN17||chrG18||chr\ O20||chrR21||chrR23||chrI24||chrS25||chrI26||chrN27||chrG28&&y>0.4&\ &y<0.53 test=test1||test2 test0=test0&&whitesq test0=((test0||test)==0) f1=fn1(imag(p5))*fn2(imag(p4))*pixel f2=real(p5)*pixel pixel=(test==0)*f1+test*f2 p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0) ; Import of formula 'mmix3' from file MMIX4-3.FRM from Jim Muth ;p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0) a=real(p_p1), b=imag(p_p1), d=real(p_p2), f=imag(p_p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p_p3)+1, l=imag(p_p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } ;****************************************************************** frm:e-viva-c { ; lake-transformation = Sylvie Gallet, Jan 16, 2000 ; requires: float=on, Fractint 20.0.6, periodicity=0' and 'passes=1' ; real part of p1: diameter of text bailout ; imag part of p1: position of text bailout (x and y) ; real part of p2: merging of text (position) ; imag part of p2: merging of text (position) ; real part of p3: x-position of text bailout versus background ; imag part of p3: y-position of text bailout versus background ; real part of p4: 0 = lake transform disabled ; any value between 0 and 100: water level in % of ; the screen height (0 = bottom, 100 = top) ; Try fn1=recip, fn2=ident: If (A=B*C) then text=invisible, else=visible! ; imag part of p4: A (position of text & picture bailout) ; real part of p5: B (position of text bailout) ; imag part of p5: C (position of picture bailout) ; to position text into the picture, try e.g.: A=0.18, B=0.18005, C=1 ; finaly set B to the best value found by 'try and error' pp_p3 = (0.2,300) ; 0.2=amplitude and 300=frequency of the lake ; Lake transformation ; ------------------- if (real(p4) > 0 && real(p4) <= 100) level = real(p4) / 100 ; water level ampl = real(pp_p3) ; amplitude of the wave freq = imag(pp_p3) ; frequency angle = real(rotskew * pi / 180) exp_irot = exp(-flip(angle)) h = 1 / real(magxmag) w = h / 0.75 * imag(magxmag) tanskew = tan(imag(rotskew * pi / 180)) u = 2 * w * exp_irot v = 2 * h * (tanskew + flip(1)) * exp_irot z3rd = center + (-w-h*tanskew - flip(h)) * exp_irot z = pixel - z3rd b = imag(conj(u)*z) / imag(conj(u)*v) if (b <= level) dy = level - b z = z + 2*dy * (1+ampl*sin(freq*dy^0.2)) * v endif pixel = z + z3rd endif z=(sinh(sinh(sinh(pixel-p3)-real(p1))-p2))/imag(p1) x=real(z), y=imag(z) ;Text = generated with FRACTEXT.EXE from J.M.v.d. WALK chrE1 = x<-0.54802||y<0.6195||(y<0.68475&&y>0.66525)||y>0.7305&&x>-\ 0.56752&&x<-0.48802 xCV=3.5*x chrV3 = y>-xCV-0.64308&&y<-xCV-0.5721||yxCV+1.7721 chrI4 = x>-0.27703&&x<-0.25753 chrV5 = y>-xCV-0.09885&&y<-xCV-0.02787||yxCV+1.2278\ 7 xCA=3*x chrA6 = y>xCA+0.90293||y>-xCA+0.5354||(y<0.66&&y>0.6405)&&y0.66525)||y>0.7305&&x>0.08902&&x<0\ .16852 chrO9 = abs(cabs(z+(-0.25852,-0.675))-0.06525)<0.00975 chrT10 = y>0.7305&&x>0.34852&&x<0.44302||(x>0.38602&&x<0.40552) chrD11 = x<0.47752||y<0.6195||y>0.7305&&x>0.45802&&x<0.49252||(abs(\ cabs(z+(-0.49252,-0.675))-0.06525)<0.00975&&x>=0.49252) test1 = chrE1||chrV3||chrI4||chrV5||chrA6||chrF8||chrO9||chrT10||ch\ rD11&&y>0.6&&y<0.75 chrE12 = x<-0.6137||y<0.4156||(y<0.4728&&y>0.4572)||y>0.5144&&x>-0.\ 6293&&x<-0.5617 chrV14 = y>-xCV-1.16296&&y<-xCV-1.10617||yxCV+1.906\ 17 chrI15 = x>-0.38019&&x<-0.36459 chrV16 = y>-xCV-0.70057&&y<-xCV-0.64379||yxCV+1.443\ 79 chrA17 = y>xCA+1.09492||y>-xCA-0.08425||(y<0.452&&y>0.4364)&&y0.4572)||y>0.5144&&x>-0.06697&&x<\ 0.00063 xCR=2*x chrR20 = y<0.4728&&y>0.4572||y>0.5144||x<0.02923&&x>0.01363&&x<0.05\ 523||(abs(cabs(z+(-0.05523,-0.4936))-0.0286)<0.0078&&x>=0.05523)||(\ y<0.465&&y<-xCR+0.58326&&y>-xCR+0.54837) chrA21 = y>xCA+0.03678||y>-xCA+0.97388||(y<0.452&&y>0.4364)&&yxCC+0.17926||y<-xCC+0.75074) chrT23 = y>0.5144&&x>0.3447&&x<0.4253||(x>0.3772&&x<0.3928) chrI24 = x>0.4383&&x<0.4539 xCN=2.5*x chrN25 = x>0.4669&&x<0.4825||(x>0.5189&&x<0.5357)||(y>-xCN+1.69725&\ &y<-xCN+1.73926) chrT26 = y>0.5144&&x>0.5487&&x<0.6293||(x>0.5812&&x<0.5968) test2 = chrE12||chrV14||chrI15||chrV16||chrA17||chrF19||chrR20||chr\ A21||chrC22||chrT23||chrI24||chrN25||chrT26&&y>0.4&&y<0.53 test=test1||test2 test0=test0&&whitesq test0=((test0||test)==0) f1=fn1(imag(p5))*fn2(imag(p4))*pixel f2=real(p5)*pixel pixel=(test==0)*f1+test*f2 p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0) ; Import of formula 'mmix3' from file MMIX4-3.FRM from Jim Muth ;p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0) a=real(p_p1), b=imag(p_p1), d=real(p_p2), f=imag(p_p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p_p3)+1, l=imag(p_p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } ******************** cheers, Guy Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 11-04-01 (Veiled Objects [7]) Date: 11 Apr 2001 08:21:31 EDT Classic FOTD -- April 11, 2001 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD is late again . . . no surprise in that. I'm still busy. But I have finally managed to find an image that rates above a 6. True, at a rating of 7, it's only a single step above 6, but it's a start. I named the image "Veiled Objects" when I noticed that the smaller features seem to be draped over the larger objects like a gossamer veil. To create the image I unpacked number 6 in my series of 12 MandNewt formulae. This formula is a random variation of the Ikenaga function, and the Ikenaga function is a minor mystery. The image takes 8-1/2 minutes to render at a low-resolution SF5, but the highest resolution available is needed to do it justice. The image may be seen by running the parameter file at the resolution of your choice, or by downloading the GIF file from: or from: once it has been posted. The fractal weather today was cloudy but dry, with a temperature of 68F (20C). The fractal cats approved of the conditions. That's it for today. I've got a busy day ahead of me, and it's time to get to work. Until next time, take care, and hug at least one fractal every day. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Veiled_Objects { ; time=0:08:38.44--SF5 on a P200 reset=2001 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 center-mag=0.277319/-1.04425/35.70909/1/82.499 params=-2.37/2.17/-1.56/-1.05/3.29/-3.17 float=y maxiter=254 inside=bof60 logmap=yes periodicity=0 colors=000jwpjwqjwqhuogsmfqlepjdniclgajf`id_gcZeaY\ c`XbZV`YUZWTXVSWTRUSQSQOQPNPNMNMLLKKJJJIHHGGGEEFCD\ EBBD9AC78945B67D78F8AH9BJACLBENCFODGQEISFJUGKWHMYI\ N_JO`KQbLRdMSfNUhOVjPWlQYmRZoS_qTasUbuVcwWexXfxYgr\ ZdkZadZ_XZXQZVJZSAYRCZQDaNFeKGhHIlEInBJoCKoCKoCLoC\ LoCMoCMoCNoCNoDOoDOoDPoDQoDQoDRoDRoDSoESoEToEToEUo\ EUoEVoEWoEWoFXoFXoFYoFYoFZoFZoF_oF_oF`mG`lH`kIajIa\ hJagKafLbeLbdMbbNbaOc`Oc_PcYQcXRdWRdVSdUTdSUeRUeQV\ ePWdMYeOWeQVeRTeTSeUQeWPeXOeZMe_LeaJebIedHeeFegEeh\ CejBekAdj9dj9cj9cj8cj8bj8bi8bi7ai7ai7ai7`i6`i6`h6_\ h6_h5_h5Zh5Zh4Yh4Yg4Yg4Xg3Xg3Xg3Wg3Wg2Wf2Vf2Vf2Vf1\ Uf1Uf1Uf1Te3Td4Td5Tc6Tc7Tb8Tb9TaBSaCS`DS`ES_FS_GSZ\ HSZJSYKSYLRXMRXNRWORWPRVQRUSRUTRTURTVQSWQSXQRYQR_Q\ Q`QQaQPbQPcQOdPOePNgPNhPMiPMjPLkPLlPKmPKnRMmTNmUOm\ WQmXRlZSl`UlaVlcWkdYkfZkh_kiajkbjlcjnejpfiqgisiitj\ ivkhxmhxnhxohkunkunkvojvp } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) C-FOTD 11-04-01 (Veiled Objects [7]) Date: 11 Apr 2001 13:28:18 -0000 >From: JimMuth@aol.com >Subject: (fractint) C-FOTD 11-04-01 (Veiled Objects [7]) >Date: Wed, 11 Apr 2001 08:21:31 EDT > >Classic FOTD -- April 11, 2001 (Rating 7) > >This formula is a random >variation of the Ikenaga function, and the Ikenaga function is a >minor mystery. What the heck is the Ikenaga function?!?! _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) Fractint Development Date: 11 Apr 2001 13:35:54 -0000 >From: Programmer Dude >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >Subject: Re: (fractint) Fractint Development >Date: Wed, 04 Apr 2001 10:58:32 -0500 > >No one has responded to this in a couple days, so I thought I'd take a >shot at it... Thanks. >Andrew Coppin wrote: > > > So, you mean that FractInt can as such only use 64KB of memory? > >Sort of. > >FractInt was born as an MS-DOS program, and MS-DOS ran on Intel chips. >Intel chips see memory as "segmented" rather than "flat" (as the Motorola >chips (used in Apple machines) do). Flat memory looks like one huge >"address space". For any memory location from 0000000 to umpteenzillion, >the memory location just refers to the appropriate point, like milage >along a road. > >In segmented memory, a memory location consists of two numbers: a >segment and an offset. The segment is like a rolling window that jumps >in, IIRC, 256-byte jumps: segment 0 starts at 0, segment 1 starts at 256, >and so on. And a segment is a 64-k "window". The offset refers to any >location within that 64-k window. > >The Intel chips ran programs in an architecture that had four segments: >a "Code" segment, a "Data" segment, a "Stack" segment and an "Extra" >segment sometimes used as a second, extended Data segment). Due to the >nature of the C language (a primary development language of the day), >the Stack and Data segments usually had to be identical. You ended up >with a 64-K window with your data growing from the bottom upwards and >your stack growing from the top downwards. The space in the middle was >the "heap" and is where you got dynamically allocated memory from. > >The "Memory Model" is what various configurations of the segments is >called. Remember the old .COM programs? By definition, they always >use the "Tiny" memory model. All segments are identical, and your >entire program--data and code--must fit in a single 64-K window. > >The "Medium" memory model, IIRC, has the stack and data sharing one >64-K segment, while the code lives in its own 64-K segment. > >This doesn't mean the program can't access data outside these segments. >It can, but outside memory is "far" in the language of Intel memory >models (opposed to the "near" memory in the data/stack segment). Because >the data/stack segment is "framed" by the segment pointers of the Intel >architecture, you only need 16 bits (64-K) to address it. But since "far" >memory is 'somewhere in address space' you need a full address which was, >at the time, 24 bits usually expressed as two 16-bit values with 8 bits of >overlap. Added together, they form a 24-bit address. > >The bottom line is that, in your program, you have a mix of "near" data >and "far" data, and they require different variable types to refer to. So it's an address space thing? What you're saying is that for certain address ranges you can miss out a couple of the MSBits? (Hence presumably smaller/faster code?) > > What's involved in such a change? Is it just a case of going through the > > program and changing half a million lines of code on a find-and-replace > > basis, or does it require an actaul redesign of the code? > >I can't speak for the FractInt developers, and I'm not familiar with the >code. I can guess it lies between those two ideas. It's not a simple >matter of S&R; I'd guess you want to examine every place you need to change >to see if the change breaks anything. But it probably does NOT require a >complete redesign. > >Ideally you'd like a compiler that let you treat memory as flat and make >all your pointers be the same type. I have no idea if such exists for >the Intel platforms. Can't you just treat everything as "far"? >But then *I* think what you *really* want is to get away from MS-DOS. > > > I'd really prefer FractInt to remain a DOS program, or perhaps to have > > a DOS *and* a Windows version. (...and a Linux/UNIX version, like they > > do with POV-Ray. Hey... isn't that a Stone Soup project too?) > >Don't *think* POV-Ray (great program, BTW) is Stone Soup. There's actually >a great concept there. POV-Ray renders to a disk file normally. The >Windows version just happens to have the extra treat of showing you the >image as it's rendered. But the heart of POV-Ray is a command line tool >for rendering 3D scenes into an image file of some type. Yeah, POV-Ray = utterly cool program! Actually, the DOS and Amiga verisons show you previouse too (unless you turn it off). > >> The other problem is that we do indeed use extended and/or expanded > >> memory for options other than just disk video. Saving the on screen > >> image when switching to a menu comes to mind. > > > > If you had more memory to play with, could this be avoided? (I >understand > > that disk video can use insane quantities of RAM, but keeping a copy of > > the video buffer for a normal screen shouldn't be too bad...) > >But what I imagine they have to save is the fractal image while the menu >screens are displayed. That could be considerable. > >Anyway, hope this little data dump helped rather than confused... Hmm... I remember back on the old 6502 processor found in the legendary C64 there was a "zero page" addressing mode, which only required an 8-bit address instead of the usuall "absolute addressing" which required a 16-bit address. I think you're saying the Intel CPU has a "base-offset" register or something that lets you use shorter addresses (and limits your address space). Close? Thanks. Andrew. PS. I am now in possetion of the fractint source code. I'll spend some time failing to understand it later... _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 11 Apr 2001 09:54:18 EDT Andrew Coppin asked: >What the heck is the Ikenaga function?!?! That's the minor mystery! The function is mentioned in the fractint.frm file, but no one seems to know where the function came from or whether it has any use other than creating fractals. There is an Ikenaga page on the 'net, but the owner of that page denies being the function's originator. Jim M. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) Re: C-FOTD 09-04-01 (Mandelbrot Mayhem [5]) Date: 11 Apr 2001 10:03:34 EDT The Programmer Dude wondered: >Why should there *be* an ultimate fractal? Seems kind of limiting... There is no 'ultimate' fractal. I intended the statement to be taken ironically. Jim M. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Programmer Dude Subject: Re: (fractint) Fractint Development Date: 11 Apr 2001 10:13:07 -0500 Andrew Coppin wrote: >> The Intel chips ran programs in an architecture that had four segments: >> a "Code" segment, a "Data" segment, a "Stack" segment and an "Extra" >> segment (sometimes used as a second, extended Data segment). >> >> The "Memory Model" is what various configurations of the segments is >> called. >> >> The "Medium" memory model, IIRC, has the stack and data sharing one >> 64K segment, while the code lives in its own 64K segment. >> >> This doesn't mean the program can't access data outside these segments. >> It can, but outside memory is "far" in the language of Intel memory... > > So it's an address space thing? What you're saying is that for certain > address ranges you can miss out a couple of the MSBits? (Hence presumably > smaller/faster code?) You can miss out on eight of them, yes. >> Ideally you'd like a compiler that let you treat memory as flat and make >> all your pointers be the same type. > > Can't you just treat everything as "far"? Yes, and I'm sure this is what the developers would like to do. It does require a re-write, since it was NOT done this way originally. Remember the age of FractInt; back then speed was an issue (well, it still is), and universal far addressing was often significantly slower depending on the compiler, compiler libraries and how you went about it. As has been mentioned, even back then, there were MS-DOS "extenders" that could present a flat address space to the system, but your compiler needed to know about it to use it. > Hmm... I remember back on the old 6502 processor found in the legendary C64 > there was a "zero page" addressing mode, which only required an 8-bit > address instead of the usuall "absolute addressing" which required a 16-bit > address. I think you're saying the Intel CPU has a "base-offset" register or > something that lets you use shorter addresses (and limits your address > space). Close? Yes. In fact, it has four (mentioned in the first paragraph above). It allows you to use 16-bit addresses with the tradeoff that you only get a 64K address space. Unlike the 6502, your "segment" can start at any 256 byte boundary in the total address space. -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) C-FOTD 11-04-01 (Veiled Objects [7]) Date: 11 Apr 2001 13:10:58 -0400 >> I named the image "Veiled Objects" when I noticed that the smaller features seem to be draped over the larger objects like a gossamer veil. = << It reminds me of a spacecraft orbiting around a planet. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 12-04-01 {Blueberries [5]) Date: 12 Apr 2001 08:31:49 EDT Classic FOTD -- April 12, 2001 (Rating 5) Fractal visionaries and enthusiasts: With today's fractal, which pictures a midget in the land of Z^sqrt2+C, we slip back to a rating of 5. This perfectly average picture features a perfectly normal, though fractured, midget that exists in a remote valley of its parent fractal. I visit the Z^sqrt2 figure frequently because in this figure the midgets are relatively easy to find compared to the midgets in other figures with exponents of Z between 1 and 2. Since 1.4142 is the square root of 2, the midgets in the Z^1.4142 figure reveal their hiding places by being surrounded with the same two-way symmetry that reveals midgets in the classic Z^2+C figure. But in the Z^1.4142 figure the midgets lie far deeper and farther apart. I named the image "Blueberries" when I noticed the berry-like depressions surrounding the barely visible midget at the center. There are roughly 9 berries in the outer ring and roughly 13 berries in the smaller inner ring, which is not at all surprising, since 13/9 equals roughly 1.4142. The parameter file takes over 23 minutes to render on a 200mhz Pentium machine. It will run faster on a faster machine, but not so fast as to make a download of the GIF image file superfluous. That image file may be found on the Web at: and at: The fractal weather today featured a steady rain from dawn to dusk. The temperature of 52F (11C) combined with the rain to keep the cats snug indoors in their beds. Once again we come to the end of the FOTD. It was a relatively brief one because I'm still busy. But eventually I'll catch up, and then, anything could happen. Until next time, take care, and help preserve fractals from extinction. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Blueberries { ; time=0:23:16.75--SF5 on a P200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-1.04105767849226400/-1.142969742678717\ 00/1.290666e+007/1/90 params=1.414213562373/0/100/0 float=y maxiter=2800 inside=0 logmap=569 periodicity=10 colors=000GU0GU0ET0CQ0AO08M06K04I02G00D00D00B00900\ 60050020020000000000000000000000000000000000000000\ 0000000200200400400400600620640840860A80A80AA0CC0C\ E0CE0EG0EH0GH2GJ2GL2HL4HN4HP6JR6JR8LT8LVALVANXCNZC\ NZEP`EPbEPbCRdCRdATdATd8Vd8Vd6Vd6Xd4Xd4Ze2Ze2Ze0`e\ 0`e0be0be0be0de0de0eg0eg0gg0gg0gg0ig0ig0kg0kg0kg0m\ i0mi0oi0oi0oi0qi0qi0si0si0uk0si0sg0qg0qe0oe0od0ob0\ mb0m`4k`6kZAiZCiXGiVHgVLgTNeTReRTeRXdP`dNbbNebLg`L\ k`Jm`HqZHsZGvXGxXEzVEzVCzVAzTAzT8zR8zR6zN4zR6zV8zX\ 8z`AzbAzeCzgCzkEzmEzqGzsGzvHxxHvzJuzJszLszLozNmzNk\ zNizNgvNeuPdsPbqP`mPZkPXiPVgRTdRRbRP`RNZRNZTLXRJXR\ JXPHVPGYNG`NEcNEfLCiLAfJAcJ8_J6WI6SJ4PK4ML2JM0GN0D\ O0AP0AQ0AR0AS0AT0AU0AV0AW0CX0EY0GZ0G_0E`0Ga0Gb0Gc0\ Gd0He0Hf0Hg0Hh0Ji0Jj0Jk2Jl2Lm4Ln6Lo8Lp8NqANrCNsENt\ EPuGPvHPwJPxJRyLRzNRzPRzPTzRTzTTzVTzVVzXVzZVz`Vz`V\ zbTzdTzdTzeTzeTzgTzgRziRz } frm:MandelbrotBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 12 Apr 2001 19:54:54 -0500 > That's the minor mystery! The function is mentioned in the fractint.frm > file, but no one seems to know where the function came from or whether it has > any use other than creating fractals. From the ikenaga.frm file that came with FRAC'Cetera volume 2 issue 7 (Jon Horner's publication): IKENAGA - Formula originally discovered by Bruce Ikenaga, at Western Reserve University, Indiana. Documented in Dewdney's `Armchair Universe". The Ikenaga set is: Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C where: Z(n) = x + yi and C = a + bi Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Bill Jemison Subject: (fractint) Jonathan - puzzling par Date: 12 Apr 2001 23:15:35 -0400 Jonathan, I can't get the following par to generate at any higher res that SF5 (640x480x256). Is this a bug? or is something going on that I am missing? *************************************************** billtest { ; Version 2001 Patchlevel 6 reset=3D2001 type=3Dlorenz passes=3Dd center-mag=3D+0.00000000000000000/+15.00000000000000000/1.333333/1.3333= params=3D0.02/5/15/1 float=3Dy maxiter=3D1000 fillcolor=3D0 inside=3D0 outside=3D0 cyclerange=3D1/1 sound=3Dbeep/fm orbitdelay=3D1000 showorbi= t=3Dyes colors=3D000pdQ0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKK= KOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>z= V\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S= 0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSK= K\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<= 3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88= G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFB= G\ GBFGBDGBCG000<6>000 } **************************************************** Bill Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 13-04-01 (Squirt [6]) Date: 12 Apr 2001 23:42:46 EDT Classic FOTD -- April 13, 2001 (Rating 6) Fractal visionaries and enthusiasts: It's been another very busy day here at Fractal Central, but not so busy that I needed to forego my daily fractal search. It was however too busy for the enlightening philosophy that you've all been waiting for. But there's a long future ahead, and the philosophy will come at the proper time. (I don't want to solve the riddle of the universe too soon -- that would take all the fun out of it.) Today's fractal is named "Squirt". I gave it this name because the image pictures another midget in the Z^(sqrt2)+C Mandeloid, and the Fractint abbreviation for 'square root' is 'sqrt', and if the letters u and i are added to the middle of 'sqrt', the word becomes 'squirt'. Another reason is that I often pronounce 'square root' as 'squirt'. The image, which vaguely resembles an octopus or starfish, is a bit above average, just enough to deserve the rating of 6 that I gave it. These 'squirt' midgets are becoming more interesting as I develop the knack of finding them. And the Z^(sqrt2)+C figure, unlike the familiar Z^2+C figure, is infinite in its surface extent. The attached parameter file takes 29 minutes to render on an aging Pentium running at 200mhz. Newer and faster machines will render the image in far less time. Older, slower ones will take far longer. Regardless, the GIF file of the image will soon be posted to: and to: The fractal weather today was partly cloudy with an afternoon temperature of 66F (19C). These conditions must have suited the dynamic duo of cats perfectly, since they spent the entire afternoon basking in the on-again off-again sunshine. As for me, I spent the afternoon trying to work my way through the backlog, having only minor success. Well, I see it's now time to shut down the fractal place and call it a night. Until next time, when I'll return with more goodies, take care and be ever vigilant for that once-in-a- lifetime fractal. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Squirt { ; time=0:29:41.84--SF5 on a P200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.91532246418772030/+0.387841135413711\ 50/2.102521e+012/1/90 params=1.414213562373/0/120/0 float=y maxiter=2800 inside=0 logmap=890 mathtolerance=/1 periodicity=10 colors=000IgmEzwEzwEzwGzxGzxGzxGzzGzzHzzHzzHzzHzzJ\ zzJzzJzzJzzKzzJzzJxzJwzJtxJrwJouJlrJkqJhoJfnJckJbi\ J_hJXeJVcHSbHQ`HNYHKXHJVHGSBEQ8BPBAN77K24J02HH0EH0\ DH0BH0AJ0BK0BM2DN5DP7EQAESDETGGVHGXKHYNH_QH`TJbVJc\ YKe`KfcKheMihMkkNlnNloNlnNlnMklMkkMkkKiiKiiJihJihH\ hfHheHheGfcGfcEfbEfbEe`Ge`Hc_Jc_KcYMbYNbXPbXQ`XS`V\ T`VV_TX_TY_S_YS`YS`YQbXQcXPeXPfVNhVNiVMkTMlTMnTKoS\ KqSJrSJtQHuQHwQHwPKuPMuPPuNQtNTtNVtNYrM_rMbrMcqMfq\ KhqKkoKloJooJqnJtnJunHxlHzlHzlHzlJznJznKxoKwoMtqMr\ qNqrNorNlrPktPitQhuQeuScwSbwT`xTYxTXxVVzVTzXQzXPzY\ NzYMz_MzYKzXKzXJzVJzVHzTHzTGxSGxQExQExPDzUDzZPzcUz\ UPzUEzK8zJ8xJ7tH7qH5lG5iG4eE4bD2_D2YB1YB1XA0_A0`80\ c50i80iB0fE0cH1`K1YM2XP4TS4QV5NY5K`7Hc4Hb7G`AG_BEY\ EEYHDXJDVMDTPBSQBSTAQVAPY8N`8Mb8Me7Kh7Ji5Hl5Hn5Go4\ Eq4Dr4Br4At48u47u45w44x42z42z21z20z20z20z20z20z20z\ 20z20z20z10z20z40z40z50z7 } frm:MandelbrotBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Multiple Bogeys" Subject: Re: (fractint) Fractint Development Date: 13 Apr 2001 03:57:28 -0400 ------=_NextPart_001_0000_01C0C3CD.DC545440 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > Can't you just treat everything as "far"? Sure, which solves problems of total available memory. But you still get = problems trying to maintain any contiguous data structure (e.g. array) sp= anning more than 64kb. With flat memory this is as easy as smaller data s= tructures.
Get Your Private, Free E-mail from MSN Hotm= ail at http://www.hotmail.com.
=

------=_NextPart_001_0000_01C0C3CD.DC545440 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
> Can't you= just treat everything as "far"?
Sure, which solves proble= ms of total available memory. But you still get problems trying to mainta= in any contiguous data structure (e.g. array) spanning more than 64kb. Wi= th flat memory this is as easy as smaller data structures.
&nb= sp;
 


Get= Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

------=_NextPart_001_0000_01C0C3CD.DC545440-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Jonathan - puzzling par Date: 13 Apr 2001 07:56:34 -0500 Bill, > I can't get the following par to generate at any higher res that SF5 > (640x480x256). > Is this a bug? or is something going on that I am missing? Here is an excerpt from lorenz.c: >> /* BAD_PIXEL is used to cutoff orbits that are diverging. It might be better to test the actual floating point orbit values, but this seems safe for now. A higher value cannot be used - to test, turn off math coprocessor and use +2.24 for type ICONS. If BAD_PIXEL is set to 20000, this will abort Fractint with a math error. Note that this approach precludes zooming in very far to an orbit type. */ #define BAD_PIXEL 10000L /* pixels can't get this big */ << Setting BAD_PIXEL to 20000 does let your par generate. I suspect that upon further zooming in, the same thing will happen. IMO, this qualifies as a bug. Although I'm not sure what we would gain by being able to zoom into these types. Tim may have more insight into what the problem is. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: DeBow Freed Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 13 Apr 2001 11:28:54 -0500 Thanks to Jonathan!

A Bruce Ikenaga currently on the Math Faculty at Millersberg, PA last year denied any knowledge or authorship of the IF's. I was unable to locate any other "Ikenaga" in the US, Europe or Japan using various Mathematical Society Membership Records available at this January's Joint Math Meeting in New Orleans.

Are their two Bruce Ikenaga's, both teaching math at US universities? Maybe this is akin to expressing surprise that there are 2 John Smith's selling pork bellies in Chicago, but I don't know common the name Ikenaga is, nor the joint probability of first name Bruce and being a practicing Math academic.

Perhaps the "Veiled Object" is really just Ikenaga.
 

Freed
 
 

Jonathan Osuch wrote:

> That's the minor mystery!  The function is mentioned in the fractint.frm
> file, but no one seems to know where the function came from or whether it
has
> any use other than creating fractals.

>From the ikenaga.frm file that came with FRAC'Cetera volume 2 issue 7 (Jon
Horner's publication):

  IKENAGA - Formula originally discovered by Bruce Ikenaga, at Western
Reserve
  University, Indiana.  Documented in Dewdney's `Armchair Universe".

          The Ikenaga set is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
          where:                      Z(n) = x + yi and C = a + bi

Jonathan

--------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   fractint@lists.xmission.com
Get Commands:   majordomo@lists.xmission.com "help"
Administrator:  twegner@fractint.org
Unsubscribe:    majordomo@lists.xmission.com "unsubscribe fractint"

Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 13 Apr 2001 11:38:14 -0500 DeBow Freed wrote: > > Are their two Bruce Ikenaga's, both teaching math > at US universities? No, it is the same person. All details may be found at his home page and the associated web pages (see the page on Biographical Information): http://www.millersv.edu/~bikenaga/ Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: DeBow Freed Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 13 Apr 2001 12:07:16 -0500 Thanks Paul.

Ikenaga's response to my query last year (and I believe his homepage also lists) one fairly lengthy Adobe-ized set of "classnotes" concerning Fractals which he (Ikenaga) stated were "trivial".

He also said he had, indeed, heard of a program called "Fractint", which he liked, and perhaps would take a look at some of last year's pod of Ikenaga-based FOTD's from Jim (which I forwarded to him) and some the Discussion Group pages. Subsequently, no mas was ever heard from Dr. Ikenaga.

He twice denied any recollection of having produced anything substantive.
Perhaps we should let him in on the secret.

DeBow

"Paul N. Lee" wrote:

DeBow Freed wrote:
>
> Are their two Bruce Ikenaga's, both teaching math
> at US universities?

No, it is the same person.  All details may be found at his home page
and the associated web pages (see the page on Biographical Information):

       http://www.millersv.edu/~bikenaga/

Sincerely,
P.N.L.
--------------------------------------------------------------
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

--------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   fractint@lists.xmission.com
Get Commands:   majordomo@lists.xmission.com "help"
Administrator:  twegner@fractint.org
Unsubscribe:    majordomo@lists.xmission.com "unsubscribe fractint"

Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Bill Jemison Subject: (fractint) Jonathan - puzzling par Date: 13 Apr 2001 13:07:04 -0400 Thanks Jonathan (although I don't have a clue as to what you are talking = about ) As you may have surmised, my reason for zooming into this = type fractal is strictly for sound-generation purposes. = ************************ > I can't get the following par to generate at any higher res that SF5 > (640x480x256). > Is this a bug? or is something going on that I am missing? Here is an excerpt from lorenz.c: >> /* BAD_PIXEL is used to cutoff orbits that are diverging. It might be = better to test the actual floating point orbit values, but this seems safe for = now. A higher value cannot be used - to test, turn off math coprocessor a= nd use +2.24 for type ICONS. If BAD_PIXEL is set to 20000, this will abort Fractint with a math error. Note that this approach precludes zooming in very far to an orbit type. */ #define BAD_PIXEL 10000L /* pixels can't get this big */ << Setting BAD_PIXEL to 20000 does let your par generate. I suspect that up= on further zooming in, the same thing will happen. IMO, this qualifies as a= bug. Although I'm not sure what we would gain by being able to zoom into= these types. Tim may have more insight into what the problem is. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ----------------------- Internet Header -------------------------------- Sender: owner-fractint@lists.xmission.com Received: from lists.xmission.com (lists.xmission.com [198.60.22.7]) by spdmgaad.compuserve.com (8.9.3/8.9.3/SUN-1.9) with ESMTP id = IAA03555; Fri, 13 Apr 2001 08:59:27 -0400 (EDT) Received: from domo by lists.xmission.com with local (Exim 2.12 #2) id 14o39G-0001EJ-00 for fractint-gooutt@lists.xmission.com; Fri, 13 Apr 2001 06:58:02 = -0600 Delivered-To: fixup-fractint@lists.xmission.com@fixme Message-ID: <000801c0c419$6e896b20$0100a8c0@bananasenior> References: <200104122315_MC2-CC59-CBE2@compuserve.com> MIME-Version: 1.0 Content-Type: text/plain; charset=3D"iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.50.4133.2400 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4133.2400 Sender: owner-fractint@lists.xmission.com Precedence: bulk Reply-To: fractint@lists.xmission.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: DeBow Freed Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 13 Apr 2001 12:20:48 -0500 To all-

Before I disseminate more misinformation than usual, Dr. Ik's "classnotes" [his phrase] on "Self-SimilarFractals" are available at the homepage address provided by PNL in the form of a Mathematica 2.1 Notebook [not Adobe, as I previously stated], which I did not have the ability to convert to legible text at the time.

When I heard nothing further from Dr. Ikenaga, I (obviously mistakenly) assumed he knew his own work better than I ever would, gave up the search for archaic versions of Mathematica software with which to translate his 2.1 Notebook, and took the man at his word.

Funny, wonder what the real genesis of the functionals was.

Freed
 

DeBow Freed wrote:

Thanks Paul.

Ikenaga's response to my query last year (and I believe his homepage also lists) one fairly lengthy Adobe-ized set of "classnotes" concerning Fractals which he (Ikenaga) stated were "trivial".

He also said he had, indeed, heard of a program called "Fractint", which he liked, and perhaps would take a look at some of last year's pod of Ikenaga-based FOTD's from Jim (which I forwarded to him) and some the Discussion Group pages. Subsequently, no mas was ever heard from Dr. Ikenaga.

He twice denied any recollection of having produced anything substantive.
Perhaps we should let him in on the secret.

DeBow

"Paul N. Lee" wrote:

DeBow Freed wrote:
>
> Are their two Bruce Ikenaga's, both teaching math
> at US universities?

No, it is the same person.  All details may be found at his home page
and the associated web pages (see the page on Biographical Information):

       http://www.millersv.edu/~bikenaga/

Sincerely,
P.N.L.
--------------------------------------------------------------
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

--------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   fractint@lists.xmission.com
Get Commands:   majordomo@lists.xmission.com "help"
Administrator:  twegner@fractint.org
Unsubscribe:    majordomo@lists.xmission.com "unsubscribe fractint"

using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 13 Apr 2001 19:40:42 -0000 >From: "Jonathan Osuch" >Reply-To: fractint@lists.xmission.com >To: >Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) >Date: Thu, 12 Apr 2001 19:54:54 -0500 > > The Ikenaga set is: Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C > where: Z(n) = x + yi and C = a + bi > >Jonathan Now *that* was what I was asking! Thanks. Andrew. _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: DeBow Freed Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 13 Apr 2001 15:35:36 -0500 Fellow Fractaliers:

FYI, what follows is a direct quote from Dr. Ikenaga's response to the second of a total of 4 messages I sent to him in September of last year attempting to inquire about "Ikenaga functions" in general, and the publication called "Self Similar Fractals" listed in his own Bibliograhy on his own Homepage in specific (addresss provided in PNL's earlier note):

"Dear Dr. Freed-

   "I wish I could be of help, but I have no idea what you're
  talking about [?????? - DBF]. If someone named something after me,
  they certainly never told me about it. :-)

    "And I've never written articles about fractals [??????- DBF]. Do you
  have references for them?

     "Also, are you sure that whoever is doing this [Jim Muth-DBF] got the name right?

     "(Thanks for mentioning fractint. I always enjoyed that program,
  but I'd thought they stopped developing it. Maybe I should go look
  again.)

  Bruce"

    After 2 more similarly confusing attempts to gain further information regarding the functions themselves or Dr. Ikenaga's publication entitled "Self-Similar Fractals" which was at that time also referenced in his own Homepage, I gave up further efforts at deciphering Dr. Ikenaga's courteous but paradoxical responses.

DeBow Freed (a/k/a DBF)

  -----
  Bruce Ikenaga                    bikenaga@marauder.millersv.edu
  Dept. of Math, P.O. Box 1002,    :::::::::::::::::::
  Millersville University,
  Millersville, PA 17551-0302

Andrew Coppin wrote:

>From: "Jonathan Osuch" <osuchj@qwest.net>
>Reply-To: fractint@lists.xmission.com
>To: <fractint@lists.xmission.com>
>Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
>Date: Thu, 12 Apr 2001 19:54:54 -0500
>
>           The Ikenaga set is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
>           where:                      Z(n) = x + yi and C = a + bi
>
>Jonathan

Now *that* was what I was asking!

Thanks.
Andrew.

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

--------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   fractint@lists.xmission.com
Get Commands:   majordomo@lists.xmission.com "help"
Administrator:  twegner@fractint.org
Unsubscribe:    majordomo@lists.xmission.com "unsubscribe fractint"

Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 14-04-01 (Squirt II [5]) Date: 13 Apr 2001 22:18:35 EDT Classic FOTD -- April 14, 2001 (Rating 5) Fractal visionaries and enthusiasts: Another busy and somewhat frustrating day has ended, to be replaced by a busy and equally frustrating evening. But at least the fractals were working right. Today's FOTD might have been named "Son of the Squirt", or "Return of the Squirt", or "Curse of the Squirt", or even "The Squirt Rises Again". All these names might have happened, but they did not. Instead I named today's image "Squirt II". I gave the fractal this unassuming name because it comes from the same Mandeloid as yesterday's image, though from a far different layer of the hyper-dimensional corkscrew caused by the multi-valued nature of the complex log function. The image, a picture of a rather gaudily colored midget in a valley of the Z^(sqrt2)+C figure, is as unassuming as its name. Because of several flaws, I could rate the image no higher than an average 5, but it's still an interesting view of things that exist in the unexplored depths of the Squirt fractal. The parameter file takes over 24 minutes to run on a 200mhz Pentium. All but the most hardy fractaliers will choose to download the GIF image file from Paul's web site at: or from Scott's site at: The fractal weather today started with a steady rain. But by 11am the rain ended and the sky cleared, leading to a sunny afternoon with a temperature of 77F (25C). The fractal cats found the conditions ideal, and showed their approval by spending the entire afternoon relaxing outdoors. My day was far from ideal, though the day's fractal partly made up for all the other things that went wrong. I'll try to have a better day tomorrow, when I'll also return with the next FOTD. Until then, take care, and perhaps I'll soon tackle the remote parts of the Zexpe (Z^2.71828...) fractal. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Squirt_II { ; time=0:24:48.96--SF5 on a P200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.72227094168292330/+0.175944088697707\ 90/1.898783e+007/1/-15 params=1.414213562373/0/33/0 float=y maxiter=4200 inside=0 logmap=630 periodicity=10 colors=000huIdsI`nGXjGUfFQbFM`EIXEESC9OC5KB3IB5K98\ M89N8CO7EQ5GR5IS4KU3MX3OY1QZ0S`0Va0Xb0Zd0`e0bh0di0\ fj0hl0jm0ln0np0pq0lm0hi8deI`bRXZ`SViORsKOzOSwRXqV`\ mYdh`hddlZfnVjsQmwMpzGtzCwz7yz3wz5uz7tz8szBqzCnyEm\ xGlwIjtJisMhqNenOdmRbjSaiU`hXYeYXdZVbaU`bSZdRYeSXd\ SVbSUbSSaSRaSQ`SO`SNZSMZSKYSJYSIXSGXSFVSEVSCUSBUS9\ SS8SS7RS5RS4QS3QS1OS0OS0NS0NS0MS0MS0KS0KS0JS0IS0GR\ 0GR0FR0ER0CR0BR09Q09Q08Q07Q05Q04Q03O03O01O00O00O00\ O00O00R00S01U03V35X57Y89ZBB`EEaGFdJIeMKfOMhROiUQjX\ SlZUmaXndYqf`sibtldunfwqhytjzwlzynzzpzymzwjztizqfz\ nezlbziazfZzdYzaVzZSzXRzUOzRNzOKyMJuJGtGFtECtB9s88\ s55s34q01q00q00q00n00m00l00j00h00f00e00d11a31`41Z5\ 3Y75X78U8BS9ERBGQCJNEMMFOKFRJGUGIXFJZEKaCMdBMf9Ni9\ Nl9Nn8Nq8Nt8Nw7Ny7Oz7Qz7Rz5Sz5Uz5Vz4Xz4Yz4Zz3`z3az\ 3bz3dz1ez1fz1fz0fz0fz0fz0fz0fz0fz0fz0fz1fz3fz4fz5f\ z4fz4fz3fz3fz3fz3fz3fz3fz } frm:MandelbrotBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Date: 14 Apr 2001 16:11:17 +1200 At 05:20 14/04/2001, you wrote: >To all- > >Before I disseminate more misinformation than usual, Dr. Ik's "classnotes" >[his phrase] on "Self-SimilarFractals" are available at the homepage >address provided by PNL in the form of a Mathematica 2.1 Notebook [not >Adobe, as I previously stated], which I did not have the ability to >convert to legible text at the time. Most of them are Postscript documents, there's only the occasional Mathematica file there (and of course "Fractals.ma" is one of them). >When I heard nothing further from Dr. Ikenaga, I (obviously mistakenly) >assumed he knew his own work better than I ever would, gave up the search >for archaic versions of Mathematica software with which to translate his >2.1 Notebook, and took the man at his word. Not that an "archaic version" would have been needed - all subsequent versions of Mathematica are capable of reading and converting pre v.3 notebooks, as can the downloadable MathReader software. >Funny, wonder what the real genesis of the functionals was. Before learning of the Dewedney reference I did a wee bit of a search - "Ikenaga" seemed fairly common, and I came up with a topologist in named Shogo Ikenaga. That looked promising, but I can't read Japanese. There was also a roboticist, who may have been another Bruce - I forget, but that didn't look very likely. Morgan L. Owens. "Most of the pages found were about Fractint's Ikenaga function." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 15-04-01 (Deep in Hyperspace [7]) Date: 14 Apr 2001 21:04:51 EDT Classic FOTD -- April 15, 2001 (Rating 7) Fractal visionaries and enthusiasts: I love vast open spaces filled with tiny distant objects, and today's image fits that description perfectly. I named the picture "Deep in Hyperspace", though the scene pictured exists obviously in everyday 3-dimensional space. It still rates a 7 however. The image is one that cries out for truecolor, but that feature is not yet available, at least in Fractint. If and when it does become available, I'll probably re-render this image as well as a batch of earlier images which suffer from the unavoidable bands. Normally, I am not bothered by bands, especially the equal-iteration bands that make a fractal a classic fractal, but occasionally, as in today's image, I would like to have perfect smoothness. I first thought of a name like "Flying Spectacles" for today's FOTD, but that name has no class whatsoever. Then I pictured myself in the vicinity of a very hot star deep in a cloud of dust. The bits and pieces floating in the foreground could only be protoplanets, so I decided on the name "Stellar Nursery". But that name has nothing to do with fractals. After a few more minutes thought, I arrived at the present name, which conveys the surreal feeling of the image quite well. The formula that created the image is number 8 in my series of 12 MandNewt formulae, which are based loosely on the Ikenaga function, the function with apparently no author to claim it. The parameter file renders in 9 minutes, making a download of the GIF file of the image more efficient. The download may be found on the W.W.Web at: and at: The fractal weather today was once again ideal, with sunny skies and a temperature of 70F (21C). The fractal cats however spent little time in the yard due to noisy sidewalk repair work at the house next door. I'm leaving now, but I shall return in 24 hours, more or less. The backlog of work is finally beginning to shrink, so the enlightening philosophy can't be too far off. Until tomorrow, take care, and don't get lost in hyperspace. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Deep_in_Hyperspace { ; time=0:08:56.89--SF5 on a P200 reset=2001 type=formula formulafile=mandnewt.frm formulaname=MandNewt08 passes=1 center-mag=0.0465338/0.0891693/27.49057/1/-82.5 params=2.945/-3.071/3.082/1.704/-3.535/2.935 float=y maxiter=250 inside=bof60 logmap=yes periodicity=0 colors=000zzzy_zx`zw`zv`zu_ztZzsYzrXzqWzpVzoUynTxm\ SwlRvkQujPtiOshNrgMqfLpeKodJncImbHlaGk`Fj_EiZDhYCg\ XBfWAeV9dU8cT7bS6aR5`Q4_P3Z7DH8EG9FFAFFBGEBHECHDDI\ DEJCEJCFKBGLAHLAIM9IN9JN8KO8LP7LP7MQ6MR6MS5MT5MU4M\ V4MW3MX3MY2MZ2M_1M`1Ma0Mb0Mc0Kd3Jd6Ie9HeCGeFEfIDfL\ CgNBgQAgT8hW7hZ6ia5id4if5hd6gb7f`8eZ9dXAcVBbTCaRD`\ PE`OF_MGZKHYIIXGJWEKVCLUAMT8NS6MT4NS5NR5OQ6OP6PO7P\ N7QM8QL8RK9RJ9SIASHATGBTFBUECUDCVCDVBDWAEW9EX8FX7F\ Y6GY5GZ4HZ3H_2I_1I`0J`0J`0Ja0Kb0Lb0Mc0Md0Nd0Oe0Pf0\ Pf0Qg0Rg1Sh1Si1Ti1Uj1Vk1Vk2Wl2Xl2Ym2Yn2Zn3_o3`p3`p\ 3aq3bq3bo9anE`lJ_kOZiTYhYXfbWegVdlVbiTagS`eQ_bPZ`N\ YZMXXKWUJVSITQGSNFRLDQJCPHAOE9NC7MA6L85OA7RC8TEAWG\ BYHC`JEbLFeNHgPIjQJlSLoUMqWOtYPvZQtYPsXPqWOpVOoUNm\ TNlTNkSMiRMhQLfPLeOKdOKbNKaMJ_KJXIIVGIVEHTDITFIUHI\ UJIVMIVOIVPIUQIURITTITUISVISWIRYIRZIQ_IQ`IPaIPcIOd\ IOeINfINhIMiIMjILkIJmJKlI } frm:MandNewt08 {; Jim Muth z=c=(pixel*p1): a=z^p2+(c-1)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) C-FOTD 15-04-01 (Deep in Hyperspace [7]) Date: 14 Apr 2001 23:00:30 -0500 JimMuth@aol.com wrote: > > The bits and pieces floating in the foreground..... > ..... The download may be found on the W.W.Web at: > > and at: > I have noticed over the past week or so, that the images created from Scott's running the "X" version of FractInt does not reproduce the level of detail with which is found in the DOS version. I usually compare the images and there was a considerable difference between several of them, especially on FOTD 13-04-01 "Squirt" (that is until Scott copied over the one from my site). But the latest image, FOTD 15-04-01 "Deep in Hyperspace" will show some of what I am talking about. My question is this, why is there so much variance between the two versions of FractInt all of a sudden?? I don't believe it was this much of a problem several months ago. Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 16-04-00 (Remotely Mandeloid [3]) Date: 16 Apr 2001 08:59:28 EDT Classic FOTD -- April 16, 2001 (Rating 3) Fractal visionaries and enthusiasts: A very busy easter Sunday left little time for fractal activity. I found time only for a quick trip to the classic Mandelbrot set, where, not surprisingly, I found a midget. The midget is located on the north shore of the bud located around -1.31, in a spiral in the third valley of a sub-radical -- a very remote location -- which is the reason I named the image "Remotely Mandeloid". Since I put next to no effort into the image, settling on the first FOTD candidate that appeared, I can rate it at only a 3. But even at a 3, it's still a midget in the M-set, almost certainly one never before seen. The area of the midget is one of near chaos, though a broad color palette reveals the familiar pattern seen in the shallow parts of valley spirals. With a render time of over 13 minutes on an old Pentium machine, the parameter file tries ones' patience. A faster way of satisfying curiosity is to download the GIF image from Paul's web site at: or from Scott's site at: And this time both sites will display the same rendered image. The fractal weather today was very pleasant most of the day, with clear skies and a temperature of 68F (20C), which lured the cats into the yard. Late in the afternoon however, clouds moved in and a chilly rain set in, cutting the cats' outdoor activities short. I've been thinking much philosophy lately. I simply have no time to write it. But eventually the wisdom or nonsense (depending on one's view of my ideas), will appear. So stay posted for more than I've had to say lately. (We really need to wake up that sleeping philofractal list.) For now it's 8:30am and back to work time. The next FOTD, a return to the MandelbrotMix4 formula, will appear in around 16 hours. Until then, take care, and from simple complex numbers mighty fractals come. Jim Muth jamth@mindspring.com START 20.0 PARAMETER FILE================================== Remotely_Mandeloid { ; time=0:13:39.72--SF5 on a p200 reset=2001 type=mandel passes=1 center-mag=-1.31202873989414700/+0.067685741726728\ 05/5.82079e+010/1/-52.492/-0.004 params=0/0 float=y maxiter=100000 bailout=25 inside=0 logmap=-11450 symmetry=none periodicity=10 colors=000UUgUUgUUhUUiUUjUUkUUlUUmUUnVUoTUpRVqPXrO\ YsM_tK`tIbsHcsIeoIflIgiIifIjcJk`JlYJnVJoSJpPJqMMrO\ OrQQrRTrTVrUXrWZrXasZcs_esagsbjsdlsensgpshoqjooknm\ lnkmnjnmhomfqldrlcslatk_ukYvkXwn_ykWsiSmfOhdKbaGX_\ CSX8MV5HS8FQAEOCDMECJGAHI9FK8DN7BP68R46T34V22X10Z0\ 4b87fGAjNGgNLdNQbNV_N`XNeVNjSNoPNtNNpMPmLRjKTgJUdI\ WaHYZG_WG`TFbQEdNDfKCgHBiEAkB9m89nGAlOBjWChcCgdFfe\ IefLegOdhQciTcjWbkZal`akc`je_ihZhjZglYgoXfqWesWdvV\ cxUczUbzVazV`zV_zVZzVYzVXzVWzVVzVUzVTzVSzVRzVtz4tz\ 4tz4tz4sz6rz7qz9qzApzCozDnzEnzGmzHlzJkzKkzLjzNizOh\ zQhzRgzSfzUezVezXdzYczZbz`bzaazc`zd_ze_zgZzhYzjXzk\ XzlYzjZzh_zf`zdazcbzacz_dzYezWfzVgzThzRizPjzNjzMiz\ LhzKgzKfzJezIdzIczHbzGazG`zF_zEZzEYzDXzCWzCVzBUzAT\ zASz9Rz8Qz8Pz7Oz6Nz6Mz5Lz4Lz4Lz4Lz4Lz4Lz4Lz5Lz5Mz5\ Mz5Mz5Mz5KzUNzRPzOSzLUzJXzIZzH`zGbzFdzEfzDizCkzBmz\ Aoz9qz8sz7tzRuzQuzPuzPuzO } END 20.0 PARAMETER FILE==================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 17-04-01 (Fractal Celebration [5]) Date: 16 Apr 2001 22:07:42 EDT Classic FOTD -- April 17, 2001 (Rating 5) Fractal visionaries and enthusiasts: Today was a day of playing catch-up here at Fractal Central. Luckily, the work actually is catching up, and though the end is not quite in sight, it is lurking just around the next corner. While catching up, I somehow managed to find time for one fractal. That image is the one that appears as today's FOTD. It's only a 5-rated image, but still worth the effort of downloading the GIF file from: or from: The iterated formula combines 15 parts of Z^(-1.1) with 1.5 parts of Z^(-13), and then adds 1/C. I named the image "Fractal Celebration" mostly in memory of my recent enjoyment of the festivities of the religious season. The fractal weather today featured cold 48F (9C) air and occasional rain. The cats tried to go outdoors, but when they saw the conditions, their noses were back inside before their tails were out. And now it's time to quickly shutter down the fractal shoppe and call it a night. But I'll return in approximately 24 hours with more fractal things. Until then, take care, and if fractals had never been discovered, I would still have faith in them. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ FractalCelebration { ; time=0:13:04.22--SF5 on a p200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.22981160230094/+1.682986998869586/3.\ 658132e+008/1/-147.5 params=15/-1.1/1.5/-13/0/300 float=y maxiter=1200 inside=0 logmap=172 periodicity=10 colors=000QX`PY_PYYPYXPYVVXT`XSdVSjVQoTPuTPySOzSMz\ SMzPPxMSrLTmIXgFYaD`XAaS7dM6fL3iA0jF0m00o00r00s03v\ 0Dy0Oz0Yz1ao3rz4jnIsyzc`fddzYVuXYxX_zX`zXczXdzXfz_\ aza_zdXzgTyjQxmOvpLssIrvFpyCoz9ixDdvI_sLVrPQpSSlOT\ gLVdIX`FXXCYT9_P4`M1`I0aD0cA0d60d30c10Y0CQ0OG0FG0F\ 40A90DC0FF3II9JMFLPJOSPPVTS__TadVdiYgo_js`lvcmxdoy\ gozipzlrzmszpszruzuvzvvzxpzrlzlgzfaz`YzVTzPOzJJzDF\ z79z14z00z0Dz0Pm0``0mM0y90z00z00m4DVGSCSfzFJzCPyAT\ u9Yp6al4fg3jc0o_0sV0xX1vX4uX7sYArYFpYIp_Lo_Om_Sl`V\ j`Yj``iadgagfajdamdYg_VaVSYQOSMLOIIIDDC9A747104009\ 01C17F4DJ6JM9PPAVSC`XFf_GlaJrfLxiOzlPzoQzi`zdis`ri\ Xz_SzQPzVOzYMz`LzcJzfIyiLvjMslOpmQomSloTipXfpYdr_a\ sa_scXudVvgSviPxjMylLydGr_MjTTcM`XGgPAiI3jA0l30m00\ o10p40r71sA4uD7vGAvJCvMFvPIxSLyVMzYGzSAzO4zJ0zF0zA\ 0z61zMFzaSzrdzzczzczzazxazvazs`zp`zm`zlazlczlczldz\ ldzlfzlfzldziczgazdazc`z` } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 18-04-01 (Fractured Fractal [6]) Date: 17 Apr 2001 23:10:15 EDT Classic FOTD -- April 18, 2001 (Rating 6) Fractal visionaries and enthusiasts: For today's fractal wonder, we turn once again to the MandelbrotBC formula, which works wonders with Mandeloids of fractional orders. I'll be using this formula often in the days to come, but unfortunately I have lost track of the formula's author. I believe the author is Andrew Coppin, though I'm not sure. Perhaps the author will claim his authorship. I noticed a flurry of mail on the fractal-art list when I opened my virtual mailbox this afternoon. The flap appears to be about another case of fractal thievery. It appears that someone was caught with someone else's fractals on their web page, and might be making money from fractals that are not theirs. Of all the things I have to worry about, copyright infringement is pretty far down the list. Maybe my lack of concern is because I feel that my fractals are not worth stealing. After all, they're only one-layered 256-color images of midgets, in a world of more colors than the eye can distinguish, and multiple layers piled on top of one another. Actually, I simply accept that my images and discussion might be stolen. If they are stolen and used for profit, and I don't know about it, I'll have nothing to get upset about. I have no time to worry about all the things that might be happening that I don't know about. If I find out about blatant profiteering from my work, then I'll know what to do and who to do it to. The mere act of posting something on the internet makes it available to anyone in the world with an online computer. And it's nearly impossible to prevent thievery. It's the artistic quandary. We want as many as possible to admire our work, yet we don't want the admirers to admire it so much that they steal it and make more money from our work than we make ourselves. While I'm trying to think of a solution to this unsolvable problem, I'll draw attention to today's FOTD, which I have named "Fractured Fractal", and which I have rated a respectable 6. The name arises from the fractured nature of the elements surrounding the mis-shapen midget. The iterated expression behind the image is Z^(2.05)+C. I have used the MandelbrotBC formula to draw a remote part of the infinite fractal created by this expression, a part that is quite chaotic and filled with almost-but-not-quite perfect midgets. The attached parameter file is slow -- 20 minutes slow. A download of the GIF image file is fast. I leave it up to the reader to decide which way to go. If they decide to take the download, the image file will be posted shortly to: and to: The fractal weather today was partly cloudy breezy and chilly, with a sunshine shower of small hail just before sunset. The temperature of 46F (8C) permitted the fractal cats only 15 minutes out of doors, leaving them testy. Well, I see it's time to shut down. I'm just starting to get things back into their familiar state of dis-organization, and I want to do a bit more of my style of organizing before I totally run out of steam. Until tomorrow, take care, and exist in peace. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fractured_Fractal { ; time=0:20:05.34--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotBC passes=1 center-mag=+1.35355495637857600/-0.015397043802760\ 70/475604.2/1/-52.499 params=2.05/0/56/0 float=y maxiter=5000 inside=0 logmap=295 periodicity=10 colors=000olLQfJPdJPcIOaIM`GL_GJYFIXFIVDGTDFSCDQCC\ PAAOAAM99L97J76I74G63F64D33D63D73DA3DC3DF1DG1DJ1DL\ 1DO1DP1DS0DT0DX0DY0D`0Da0Dd0Df0Di0Dj0Dm0Do0Dr0Ds0D\ v0Dx0Dz0Fz0Dz0Dy0Cx0Cu0As0Ap09o09l09i07g07d06c06`0\ 4_04X04V03S03P01O01L00J00G00F00C009007004003000000\ 0000000000000000100410630960A70D90GC0ID0LF0MG0PJ0S\ L0TM0XP0YQ0`S0cV1dX1gY1i_1lY1mV1oT7rQFsOMvMTxJ`zId\ zFizDmzArz9vz6vz4vz7rz9ozAvzCzzDzzFzzGzxIzvJzuMzsO\ zrPvpQyoSzlTzjVziXzgYzf`zdavccoadg_f`YgXXiYVj_Tl`S\ oaQpcOrdMsfLugJviIxjGylFzjFzlDzlCylAvmAslArlCplCol\ DmlDllFjjGijIgjJfjLdjMcjOajPajQajSaiQaiPagOagMagJa\ fIafGadFadDadAcc9cc7ca6ca3ca1c`0c`0c_0c_0c_0cY0cY0\ cX0dY0c_0c_0c`0ca0aa0ac0ac0ad0af0`f0`g0`g0`i0_j0_j\ 0_l0_l0_m0Yo0Yo0Yp0Yp0Yr0Xs0as0fu0jv0ov0sx1xx1zy1z\ z3zz3zz3zz3zz4zz4zz4zz6zz6zz6zz7zz7zz7zz7zz7zz9zzA\ zzAzzCzzDzzDzzFzzFzzGzzIz } frm:MandelbrotBC = { ; formula written by ? ? e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Date: 18 Apr 2001 00:08:41 -0500 JimMuth@aol.com wrote: > > ....we turn once again to the MandelbrotBC formula.... > ....but unfortunately I have lost track of the formula's > author. I believe the author is Andrew Coppin, though > I'm not sure. Yes, it was Andrew that first started the conversation on "Branch Cuts" back on April 07, 2000. Within about three to four days, he was able to come up with the following, as quoted from his email: _______________________________________________________________________ I now have two working formulas: ---BEGIN MandelbrotBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<4 } JuliaBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q C=p3 Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<4 } ---END Plug these into the evolver, with real(p1) changing from 2 to 3 along the X axis and real(p2) changine from -6 to +6 along the Y axis and you have a real treat of an image (depending on the other parameters; I used p3=-1). Now, if I can just remember how to do that IsMand() stuff... _______________________________________________________________________ Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Date: 18 Apr 2001 17:56:35 -0000 Thankyou paul. Yes, it was indeed I who thought of it, and [eventually] came up with the .frm text. It seems only fair to mention that I had help from others on this list thought... (Wish I could remember whom, but I definitly had help!) Thanks. Andrew >From: "Paul N. Lee" >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >CC: philofractal@lists.fractalus.com >Subject: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) >Date: Wed, 18 Apr 2001 00:08:41 -0500 > >JimMuth@aol.com wrote: > > > > ....we turn once again to the MandelbrotBC formula.... > > ....but unfortunately I have lost track of the formula's > > author. I believe the author is Andrew Coppin, though > > I'm not sure. > >Yes, it was Andrew that first started the conversation on "Branch Cuts" >back on April 07, 2000. Within about three to four days, he was able to >come up with the following, as quoted from his email: > >_______________________________________________________________________ > > >I now have two working formulas: > >---BEGIN >MandelbrotBC = { ; Z = Z^E + C > e=p1 > p=real(p2)+PI > q=2*PI*trunc(p/(2*PI)) > r=real(p2)-q > Z=C=Pixel: > Z=log(Z) > IF(imag(Z)>r) > Z=Z+flip(2*PI) > ENDIF > Z=exp(e*(Z+flip(q)))+C > |Z|<4 >} > >JuliaBC = { ; Z = Z^E + C > e=p1 > p=real(p2)+PI > q=2*PI*trunc(p/(2*PI)) > r=real(p2)-q > C=p3 > Z=Pixel: > Z=log(Z) > IF(imag(Z)>r) > Z=Z+flip(2*PI) > ENDIF > Z=exp(e*(Z+flip(q)))+C > |Z|<4 >} >---END > >Plug these into the evolver, with real(p1) changing from 2 to 3 along >the X axis and real(p2) changine from -6 to +6 along the Y axis and you >have a real treat of an image (depending on the other parameters; I used >p3=-1). Now, if I can just remember how to do that IsMand() stuff... > > >_______________________________________________________________________ > > >Sincerely, >P.N.L. >-------------------------------------------------------------- >http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go > >-------------------------------------------------------------- >Thanks for using Fractint, The Fractals and Fractint Discussion List >Post Message: fractint@lists.xmission.com >Get Commands: majordomo@lists.xmission.com "help" >Administrator: twegner@fractint.org >Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Zorba the Hutt" Subject: (fractint) The specter of schoolwork, and really really big fractals Date: 18 Apr 2001 16:33:04 -0400 Finally I managed to beat down the looming demon of Far Too Much Homework That You've Been Putting Off, You Slacker, And Why Are We Paying For You To Go To College Anyway If All You Do Is Play Computer Games? I Mean, It's Not Like The Ones You Play Are Educational Or Anything, and managed to eke out some time for myself, which I spent updating my Really Big Fractals page. Today (this week? this month? this year?), I provide for you all those Fractal-Swarm-inspired images that Sylvie Gallet posted a while back. Yes, all of them. All 9. Done in beautiful 1600x1280, and do they ever look good. And, sigh, I really should have asked *before* this, but if I ask, wait for an answer, and *then* post 'em, I'll never get around to it. Sylvie, do you mind if I put those up? They're all credited to you and everything :) I just wanted to provide them for people who might not have the CPU power (or desire) to render them on their own. If you say you do mind, I'll take 'em off immediately, or if there's modifications you want me to make or anything. Anyway, the website is http://www.geocities.com/zorbathut - may you find a new desktop wallpaper . . . -Zorba Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Programmer Dude Subject: Re: (fractint) The specter of schoolwork, and really really big fractals Date: 18 Apr 2001 15:53:44 -0500 Zorba the Hutt wrote: > ...which I spent updating my Really Big Fractals page. Cool! Wonderful!! Delightful!!! Thanks! p.s. Unexpected Fractal's link is ge-broken. ;-( -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) The specter of schoolwork, and really really big Date: 18 Apr 2001 17:43:56 -0400 Hi Zorba, >> And, sigh, I really should have asked *before* this, but if I ask, wai= t >> for an answer, and *then* post 'em, I'll never get around to it. Sylvi= e, >> do you mind if I put those up? They're all credited to you and >> everything :) I just wanted to provide them for people who might not >> have the CPU power (or desire) to render them on their own. If you say= >> you do mind, I'll take 'em off immediately, or if there's modification= s >> you want me to make or anything. I am not favorable to making high resolution images available on the we= b, and I would definitely have preferred you to ask before doing it. Since = I have a slow internet connection, I haven't downloaded any of them, but th= e size of some of the PNGs make me think that anti-aliasing made some of th= em lose their particular texture (at least two of them: 18 and 27). I'll make an exception and let you keep them but please, change the copyright notice so that it makes clear people are not allowed to print them, put them on a web site, etc. Best regards, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Date: 19 Apr 2001 00:16:05 -0500 Andrew Coppin wrote: > > Thankyou paul. Just thought credit should be mentioned where due. :-) > > It seems only fair to mention that I had > help from others on this list thought... > (Wish I could remember whom, but I definitly > had help!) You first started discussing the "Branch Cuts" on Fri, 07 Apr 2000. And some of the individuals involved with that topic on the List were as follows: Barry N. Merenoff (Collin Merenoff) Morgan L. Owens Tim Wegner Jim Muth Kenneth Childress Damien M. Jones This went on until Tue, 18 Apr 2000. I am sure that the archives will show the details of who did what. P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 19-04-01 (Pi in the Sky [6]) Date: 19 Apr 2001 10:51:09 EDT Classic FOTD -- April 19, 2001 (Rating 6) Fractal visionaries and enthusiasts: It's 9:30am and the FOTD is once again late. But what's new about that? I offer excuse number three -- that things were too busy here at Fractal Central Auxiliary to get the discussion written at the regular time. Maybe I need to get a day or two ahead in my FOTD's. That way I won't be late every time I have a busy day. Of course, the problem with this solution is that I have little time to get ahead. Today's image is a picture of a midget in the Z^(pi)+C fractal, as rendered by Andrew's MandelbrotBC formula. After a moment's consideration, I rated the image a 6 and named it "Pi in the Sky". At 4-1/2 minutes on an aging Pentium, it's not too difficult an image to render from the parameter file. But for those who would rather not render, the GIF image is, or soon will be, posted to the WWW at Paul Lee's site at: and at Scott's site at: The intrepid fractal cats had a rough day, as very un-springlike cold enveloped the area. The temperature of 42F (5.5C) was entirely too chilly for their sensitive ears, forcing them to sulk indoors all afternoon, while blaming me for the outside conditions. I finally eased their moodiness by treating them to a meal of tuna fish. When I checked my virtual mailbox first thing this morning, I found a very long letter telling me how to get rich quick. The letter is one of those pyramid chain letters with a MLM twist, which claims one can get rich by sending money to other people. Having my name and address so widespread on the net, I have been receiving different versions of this same letter for years. I usually delete it at once, but for some strange reason I decided this morning to skim through it. The letter begins by telling me that it is the letter I've been hearing about so much in the news lately. Now, I keep up pretty well with the news, but I have no recollection of ever hearing or reading about such a letter. I suppose that a reader who might take the letter seriously is supposed to think that the letter was indeed in the news, but that he missed it. Basically, the letter claims that one can become wealthy by doing nothing but sending money to others and having them send money back to you. If this were true, everyone on earth should be a USA-style millionaire by this time, though I have no idea where the extra money could come from or how inflation could be kept under control once everyone was rich. (Of course, we could blame the inflation on the political party in power.) In my experience, one gets rich by starting out doing work for others and receiving money from them in return, not by starting by sending money to others. In all my years of earning money working at real jobs, I have never started on a job by sending money to someone else in return for the privilege of working on their job. But apparently, from the frequency with which I receive this same letter, many are still out there who fail to understand this simple fact of life. Well, I seem to have gotten off the fractal topic. My intent was to discuss the current state of the Fractint program and the possibilities for its future development. This will be my topic when the next FOTD appears in only 12 hours or so. It's now time to start the day's rush. Until next time, take care, and I'm sorry Jonathan Roarke. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Pi_in_the_Sky { ; time=0:04:37.66--SF5 on a p200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.9197872859930445/-0.1300422309794571\ /5.421884e+007/1/-25 params=3.14159265358979/0/32/0 float=y maxiter=2400 inside=0 logmap=103 periodicity=10 colors=000zszzszztzzuzzvyzwvzxszyqzynyzkyziszfnyej\ sceob_j_XeZRaYNXXIQSDKQ8EN37K03J2DO3KS4UY6aa8geAog\ BvkDznHwjKsfOocSj_XfX_bUcYQgUMjQJaSISVHKXHIZFH_FFa\ EEbEDeDBfD8gD7iB6kB4mA3nA2oA8q8Fq7Kr7Rr6Xr6Yn7Yj8Z\ fAZbA_ZB_VDaRDaNEbJFbHFfJHiMImOJoRJsSKvVMzYMz_NzbO\ zcOziUwmZqqckuifyn_zsVzyQzzayjmmSybBwbDvbEubHsbIrb\ JqbM72u60w60yD0zI3zN7zSBzZFzcJziNznRzsUzuYwuaqueju\ icukZsg_sc_s__rXarUarQaqMbqIbqFboBco7co3co0ccBXUMO\ JXI8fA0o36n4Dn6Jm6Qm7Xm7So6Qq4Ns3Ju2Hv0Ey0Bz07z04z\ 02z00z00z02v03q04k36f47a78X8ARBBMDDHFEBHF6JH0KI0NI\ 0OH0NH0MH0KH0JF3IF6HF8FFBEEEDEHBEJAEM8DO7DR6DU4DX4\ DY0vZ2r_0oa0mb0ic0fe0cf0_g0Yi0Vj0Rk0Om0Mn0Io0Fq00r\ z0sw0us0vn0wj2ye3za4zX4zS6zN7zJ8zEAzABz4Dz00zv0zk2\ za4zR7zHAz6vzMqzJmzHgzEczBZz8rz0vz0yz0zz0vz0qz6kzB\ fzIbzNYzSSzZNzcJziEzo8zu3zz0zz4zzAzzFzyJzwOzuUzsYz\ qbzogzmmzkqzivzgzzezzzzzz } frm:MandelbrotBC { ; Formula by Andrew Coppin e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 19-04-01 (Pi in the Sky [6]) Date: 19 Apr 2001 10:51:09 EDT Classic FOTD -- April 19, 2001 (Rating 6) Fractal visionaries and enthusiasts: It's 9:30am and the FOTD is once again late. But what's new about that? I offer excuse number three -- that things were too busy here at Fractal Central Auxiliary to get the discussion written at the regular time. Maybe I need to get a day or two ahead in my FOTD's. That way I won't be late every time I have a busy day. Of course, the problem with this solution is that I have little time to get ahead. Today's image is a picture of a midget in the Z^(pi)+C fractal, as rendered by Andrew's MandelbrotBC formula. After a moment's consideration, I rated the image a 6 and named it "Pi in the Sky". At 4-1/2 minutes on an aging Pentium, it's not too difficult an image to render from the parameter file. But for those who would rather not render, the GIF image is, or soon will be, posted to the WWW at Paul Lee's site at: and at Scott's site at: The intrepid fractal cats had a rough day, as very un-springlike cold enveloped the area. The temperature of 42F (5.5C) was entirely too chilly for their sensitive ears, forcing them to sulk indoors all afternoon, while blaming me for the outside conditions. I finally eased their moodiness by treating them to a meal of tuna fish. When I checked my virtual mailbox first thing this morning, I found a very long letter telling me how to get rich quick. The letter is one of those pyramid chain letters with a MLM twist, which claims one can get rich by sending money to other people. Having my name and address so widespread on the net, I have been receiving different versions of this same letter for years. I usually delete it at once, but for some strange reason I decided this morning to skim through it. The letter begins by telling me that it is the letter I've been hearing about so much in the news lately. Now, I keep up pretty well with the news, but I have no recollection of ever hearing or reading about such a letter. I suppose that a reader who might take the letter seriously is supposed to think that the letter was indeed in the news, but that he missed it. Basically, the letter claims that one can become wealthy by doing nothing but sending money to others and having them send money back to you. If this were true, everyone on earth should be a USA-style millionaire by this time, though I have no idea where the extra money could come from or how inflation could be kept under control once everyone was rich. (Of course, we could blame the inflation on the political party in power.) In my experience, one gets rich by starting out doing work for others and receiving money from them in return, not by starting by sending money to others. In all my years of earning money working at real jobs, I have never started on a job by sending money to someone else in return for the privilege of working on their job. But apparently, from the frequency with which I receive this same letter, many are still out there who fail to understand this simple fact of life. Well, I seem to have gotten off the fractal topic. My intent was to discuss the current state of the Fractint program and the possibilities for its future development. This will be my topic when the next FOTD appears in only 12 hours or so. It's now time to start the day's rush. Until next time, take care, and I'm sorry Jonathan Roarke. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Pi_in_the_Sky { ; time=0:04:37.66--SF5 on a p200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.9197872859930445/-0.1300422309794571\ /5.421884e+007/1/-25 params=3.14159265358979/0/32/0 float=y maxiter=2400 inside=0 logmap=103 periodicity=10 colors=000zszzszztzzuzzvyzwvzxszyqzynyzkyziszfnyej\ sceob_j_XeZRaYNXXIQSDKQ8EN37K03J2DO3KS4UY6aa8geAog\ BvkDznHwjKsfOocSj_XfX_bUcYQgUMjQJaSISVHKXHIZFH_FFa\ EEbEDeDBfD8gD7iB6kB4mA3nA2oA8q8Fq7Kr7Rr6Xr6Yn7Yj8Z\ fAZbA_ZB_VDaRDaNEbJFbHFfJHiMImOJoRJsSKvVMzYMz_NzbO\ zcOziUwmZqqckuifyn_zsVzyQzzayjmmSybBwbDvbEubHsbIrb\ JqbM72u60w60yD0zI3zN7zSBzZFzcJziNznRzsUzuYwuaqueju\ icukZsg_sc_s__rXarUarQaqMbqIbqFboBco7co3co0ccBXUMO\ JXI8fA0o36n4Dn6Jm6Qm7Xm7So6Qq4Ns3Ju2Hv0Ey0Bz07z04z\ 02z00z00z02v03q04k36f47a78X8ARBBMDDHFEBHF6JH0KI0NI\ 0OH0NH0MH0KH0JF3IF6HF8FFBEEEDEHBEJAEM8DO7DR6DU4DX4\ DY0vZ2r_0oa0mb0ic0fe0cf0_g0Yi0Vj0Rk0Om0Mn0Io0Fq00r\ z0sw0us0vn0wj2ye3za4zX4zS6zN7zJ8zEAzABz4Dz00zv0zk2\ za4zR7zHAz6vzMqzJmzHgzEczBZz8rz0vz0yz0zz0vz0qz6kzB\ fzIbzNYzSSzZNzcJziEzo8zu3zz0zz4zzAzzFzyJzwOzuUzsYz\ qbzogzmmzkqzivzgzzezzzzzz } frm:MandelbrotBC { ; Formula by Andrew Coppin e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) The specter of schoolwork, and really really big Date: 19 Apr 2001 18:22:45 -0400 Hi Zorba, All of the images are different from their Fractint version, and in lot= s of them, UF replaced the nice texture with banding so, I'd like you to remove them or redo them with Fractint (maybe in a standard 1600x1200 format). Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Zorba the Hutt" Subject: Re: (fractint) The specter of schoolwork, and really really big fractals Date: 19 Apr 2001 21:30:27 -0400 Done. I don't know why they're different - I remember I checked some of them, and they were the same, or at least I thought they were. Perhaps it's a fractint difference also. Anyway, they're gone now - really sorry about the annoyance ^^;; -Zorba ----- Original Message ----- Sent: Thursday, April 19, 2001 6:22 PM fractals Hi Zorba, All of the images are different from their Fractint version, and in lots of them, UF replaced the nice texture with banding so, I'd like you to remove them or redo them with Fractint (maybe in a standard 1600x1200 format). Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 20-04-01 (Fairy Gardens [6]) Date: 19 Apr 2001 22:35:37 EDT Classic FOTD -- April 20, 2001 (Rating 6) Fractal visionaries and enthusiasts: Do fairies, elves, gnomes, sylphs, etc. exist? Of course they do. Every culture on earth is rich with stories and legends of fairies. But since fairies, just like dragons, do indeed exist, are they then real? The answer to that question depends on the meaning one gives to the word 'real'. Not yet being in my deep philosophical mode, I'll not at this time state my opinion of the meaning of the word 'real', but if fairies do not dwell in the intricacies of the garden-like scene of today's fractal, what then does? The formula that drew the image, TowerMinExp04a, is one I rarely use. It is but one in a remote series of 26 such formulae, which pile up the exponents of Z into exponent towers. The four functions in today's formula merely add variety. I named the image "Fairy Garden" when a lawn fairy flew past the window while I was trying to think of a name. The image is a bit too busy and fragmented for a very high rating, but the 6, which is a little above average, is satisfactory. As long as my FOTD's rate above a 5, I'm satisfied with them. I'll not divulge at this time whether I believe in magical things such as fairies, and yes even dragons. I will state however that I believe in some things that many consider weird or downright kooky. My beliefs are not limited by the discoveries of science, nor by common sense or reason, though I certainly do occasionally use these attributes. The parameter file of today's image, which is attached to the bottom of this letter, renders in 2-1/2 minutes. For extra convenience, the GIF image file is or soon will be posted to the W.W.Web at the URL: and at: I read recently that the venerable Fractint fractal generating program is over the hill, on its last lap, abandoned by all but a few backward fractalists in favor of more advanced fractal generating programs with glittery advanced features such as true-color, multiple layers, transforms, etc. Well, one would never guess it here at Fractal Central, where the old warhorse program continues to do what it was designed to do -- find fractals. It's not that I have no other programs -- three other fractal generating programs are on my drive. But I rarely use them. Other than true-color, which is Fractint's greatest lack, I feel that the other features of the state-of- the-art programs are leading us from the basic idea of fractals. We are drifting from a "look what I found" attitude to a "look Ma, I'm an artist" attitude. When the fractalist does more work on an image than the numbers, perhaps the resulting image should be called something like computer art, rather than fractal art. I guess I have never been able to make the switch from admiring the things the numbers have done to admiring the things I have done. Maybe my reluctance to embrace the newer programs is due to the fact that I had been working with graphic programs such as Photoshop long before the same image manipulating features appeared included in fractal programs, and I therefore failed to be impressed with such features. (Of course, the features are far less expensive when part of the actual fractal program.) I also find myself amused at the extreme concern on the fractal- art list about copyright infringement. Fractals are fun -- they're philosophical, mystical and scientific at the same time. They're not a means of becoming wealthy. Do we really think that someone is going to steal our fractals and get rich from our efforts? If anyone were planning to do this, they certainly would not post their stolen goods on the Web for the whole world to see. I started the FOTD almost exactly 4 years ago for the fun of it. I continue the FOTD 4 years later for the fun of it. If it were not fun, I would have grown bored with the effort years ago and stopped posting. But I have no intention of ending the FOTD in the foreseeable future, because I know that finding fractals will be as much fun in 2005 as it is in 2001 and was in 1997. The fractal weather today was a big improvement over yesterday. A warm sun brought the temperature up to 61F (16C), and brought out the fractal cats into the yard for an afternoon's romp in the new grass. The rush is easing somewhat, but there's still lots to be done. Between other stuff I'll find time for another FOTD in 24 hours. Until then, take care, and watch out for the fairies as you trim your newly greened lawn. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fairy_Gardens { ; time=0:02:30.77--SF5 on a P200 reset=2001 type=formula formulafile=tower.frm formulaname=TowerMinExp04a function=sqrt/sinh/acos\ h/tanh passes=1 center-mag=1.39458/-1.16573e-015/3\ .617023/1.0776/90 params=3.91/0/3.75/0/-3.215/0 float=y maxiter=250 inside=bof60 logmap=yes periodicity=10 colors=000zzzVLRD9Q00N00P00R00T01V13X34Y46_67a89c9\ AeBCfCDhEFjFGlHInJJoKLqMMsNOuPPwQQxPPuOOrNNoMMlLLj\ KKgJJdIIaII_HHXGGUFFREEODDMCCJBBGAADAAB7A95A82A70A\ 50A40A30900A20B40C50D70E90FA0GC0HE1IF2JH3KJ4LK5MM6\ NO7OP8PR9QTARUBSWCTYDTZJWYPYYV`Y`bXfeXkgXheWecVcbU\ ``UY_TWYSTXRQVROUQLSPIQPGPODNNAMM8KM5JL2IK0IK1KO2N\ S3QW4T_5Wb6Zf7aj8dn7fp8gq8fq8dq8bq9_q9Xq9Vq9TqARqA\ PqAMqAKqBIqBGqBEqBBqC9qC7qC5qD1sC3qC5pC7oC9nCBmCCl\ CEkCGjCIhCKgCLfCNeCPdCRcCTbDT`CUaBVaAWaAXa9Ya8Za8Z\ a7_b6`b5ab5bb4cb3db3db2ec1fc0gc0hc0ic0jc0jc0eb0`a0\ X`0S_0N_0JZ0EY09X07X05X26Y36Y47Z67Z77_88_A8`B9`C9`\ E9aFAaGAbHBbJBcKBcLCcNCdODdPDeRDeSEfTEfTEfTEfTFcTF\ `TFYTFVTFSTEPTEMTEJTDGTDETDFUCFTCGSCGQBGPBHOBHNBHP\ AHQAHR9HS9HT9HU8HW8HX8HY7HZ7H_7H`6Ha6Hc6Hd5He5Hf5H\ g4Hh4Hi4Hh1Kg0Mh0Ng0Og0Pg0Qg3Rg5Sg7TgAUgCUfEVfGWfJ\ XfLYfNZfQ_fS`fU`eWagXVjYT } frm:TowerMinExp04a {; Jim Muth z=pixel, c=p2+(p3*pixel): z=z^fn1(z^fn2(-z^fn3(z^fn4(-z+p1))))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: erdal mazlum Subject: Re: (fractint) C-FOTD 19-04-01 (Pi in the Sky [6]) Date: 19 Apr 2001 22:28:51 -0700 (PDT) hi jim, your comment about the letter is pretty cool, and FOTD ofcourse... have a nice day! erdal. --- JimMuth@aol.com wrote: > > Classic FOTD -- April 19, 2001 (Rating 6) > > Fractal visionaries and enthusiasts: > > It's 9:30am and the FOTD is once again late. But > what's new > about that? I offer excuse number three -- that > things were too > busy here at Fractal Central Auxiliary to get the > discussion > written at the regular time. Maybe I need to get a > day or two > ahead in my FOTD's. That way I won't be late every > time I have > a busy day. Of course, the problem with this > solution is that > I have little time to get ahead. > > Today's image is a picture of a midget in the > Z^(pi)+C fractal, > as rendered by Andrew's MandelbrotBC formula. After > a moment's > consideration, I rated the image a 6 and named it > "Pi in the > Sky". At 4-1/2 minutes on an aging Pentium, it's > not too > difficult an image to render from the parameter > file. > > But for those who would rather not render, the GIF > image is, or > soon will be, posted to the WWW at Paul Lee's site > at: > > > > > and at Scott's site at: > > > > The intrepid fractal cats had a rough day, as very > un-springlike > cold enveloped the area. The temperature of 42F > (5.5C) was > entirely too chilly for their sensitive ears, > forcing them to > sulk indoors all afternoon, while blaming me for the > outside > conditions. I finally eased their moodiness by > treating them to > a meal of tuna fish. > > When I checked my virtual mailbox first thing this > morning, I > found a very long letter telling me how to get rich > quick. The > letter is one of those pyramid chain letters with a > MLM twist, > which claims one can get rich by sending money to > other people. > Having my name and address so widespread on the net, > I have been > receiving different versions of this same letter for > years. I > usually delete it at once, but for some strange > reason I decided > this morning to skim through it. > > The letter begins by telling me that it is the > letter I've been > hearing about so much in the news lately. Now, I > keep up pretty > well with the news, but I have no recollection of > ever hearing > or reading about such a letter. I suppose that a > reader who > might take the letter seriously is supposed to think > that the > letter was indeed in the news, but that he missed > it. > > Basically, the letter claims that one can become > wealthy by > doing nothing but sending money to others and having > them send > money back to you. If this were true, everyone on > earth should > be a USA-style millionaire by this time, though I > have no idea > where the extra money could come from or how > inflation could be > kept under control once everyone was rich. (Of > course, we could > blame the inflation on the political party in > power.) > > In my experience, one gets rich by starting out > doing work for > others and receiving money from them in return, not > by starting > by sending money to others. In all my years of > earning money > working at real jobs, I have never started on a job > by sending > money to someone else in return for the privilege of > working on > their job. But apparently, from the frequency with > which I > receive this same letter, many are still out there > who fail to > understand this simple fact of life. > > Well, I seem to have gotten off the fractal topic. > My intent > was to discuss the current state of the Fractint > program and the > possibilities for its future development. This will > be my topic > when the next FOTD appears in only 12 hours or so. > > It's now time to start the day's rush. Until next > time, take > care, and I'm sorry Jonathan Roarke. > > > Jim Muth > jamth@mindspring.com > > > START 20.0 PAR-FORMULA > FILE================================ > > Pi_in_the_Sky { ; time=0:04:37.66--SF5 on a > p200 > reset=2001 type=formula formulafile=branchct.frm > formulaname=MandelbrotBC passes=1 > > center-mag=-0.9197872859930445/-0.1300422309794571\ > /5.421884e+007/1/-25 > params=3.14159265358979/0/32/0 > float=y maxiter=2400 inside=0 > logmap=103 periodicity=10 > > colors=000zszzszztzzuzzvyzwvzxszyqzynyzkyziszfnyej\ > > sceob_j_XeZRaYNXXIQSDKQ8EN37K03J2DO3KS4UY6aa8geAog\ > > BvkDznHwjKsfOocSj_XfX_bUcYQgUMjQJaSISVHKXHIZFH_FFa\ > > EEbEDeDBfD8gD7iB6kB4mA3nA2oA8q8Fq7Kr7Rr6Xr6Yn7Yj8Z\ > > fAZbA_ZB_VDaRDaNEbJFbHFfJHiMImOJoRJsSKvVMzYMz_NzbO\ > > zcOziUwmZqqckuifyn_zsVzyQzzayjmmSybBwbDvbEubHsbIrb\ > > JqbM72u60w60yD0zI3zN7zSBzZFzcJziNznRzsUzuYwuaqueju\ > > icukZsg_sc_s__rXarUarQaqMbqIbqFboBco7co3co0ccBXUMO\ > > JXI8fA0o36n4Dn6Jm6Qm7Xm7So6Qq4Ns3Ju2Hv0Ey0Bz07z04z\ > > 02z00z00z02v03q04k36f47a78X8ARBBMDDHFEBHF6JH0KI0NI\ > > 0OH0NH0MH0KH0JF3IF6HF8FFBEEEDEHBEJAEM8DO7DR6DU4DX4\ > > DY0vZ2r_0oa0mb0ic0fe0cf0_g0Yi0Vj0Rk0Om0Mn0Io0Fq00r\ > > z0sw0us0vn0wj2ye3za4zX4zS6zN7zJ8zEAzABz4Dz00zv0zk2\ > > za4zR7zHAz6vzMqzJmzHgzEczBZz8rz0vz0yz0zz0vz0qz6kzB\ > > fzIbzNYzSSzZNzcJziEzo8zu3zz0zz4zzAzzFzyJzwOzuUzsYz\ > qbzogzmmzkqzivzgzzezzzzzz > } > > > frm:MandelbrotBC { ; Formula by Andrew Coppin > e=p1 > p=real(p2)+PI > q=2*PI*trunc(p/(2*PI)) > r=real(p2)-q > Z=C=Pixel: > Z=log(Z) > IF(imag(Z)>r) > Z=Z+flip(2*PI) > ENDIF > Z=exp(e*(Z+flip(q)))+C > |Z|<100 > } > > END 20.0 PAR-FORMULA > FILE================================== > > > Thanks for using Fractint, The Fractals and Fractint > Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > === message truncated === __________________________________________________ Do You Yahoo!? Yahoo! Auctions - buy the things you want at great prices http://auctions.yahoo.com/ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 21-04-01 (Oriental Lanterns [7]) Date: 20 Apr 2001 22:24:43 EDT Classic FOTD -- April 21, 2001 (Rating 7) Fractal visionaries and enthusiasts: The day grew far busier far sooner than I had expected, and then the fairies returned to their fairy nests. Nothing remained for me to do but tackle the work, finish it as quickly as possible, and see what kind of a fractal I could scrounge up from the depths of infinity. I did my scrounging in the fractal created by the unassuming formula 1.25Z^(-20)+15Z^(-1.23)+(1/C), which consists of an eastward-facing Mandeloid with many spurious bays and valleys. The scene of today's midget is at the tip of the stem shooting out from a rudimentary bud on the unusually smooth north shore of the largest bay. I named the final picture "Oriental Lanterns" when I noticed that the orangish square features vaguely resemble those festive decorative lanterns. Because of the unusually brilliant color palette, I rated the image at a 7. Whether I'll still rate it a 7 next week at this time remains to be seen. The attached parameter file renders in just over 4 minutes on a somewhat tired old Pentium 200mhz machine. It will render significantly faster on a fresh young PentiumIV machine. For those who fail to enjoy the effort of running parameter files, the finished GIF image file is available on the Web at: and at: The fractal weather today turned cloudy, but the temperature reached 69F (20.5C), allowing the fractal cats a good afternoon's romp in the balmy outdoors. When a neighborhood stray intruded, the dynamic duo almost got into a fight with the intruder, but common sense prevailed, and the duo managed to stay out of trouble all afternoon. My urge to philosophize is rising, but so is the pile of work to be done. And only two days ago I thought the rush was near an end. One of these weeks I'll manage to get caught up, but this week isn't the one. So until next time, which will come in 24 hours plus or minus 2 hours, take care, and relish your fractals, but don't add onions, or you'll be in a pickle. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Oriental_Lanterns { ; time=0:04:20.78--SF5 on a p200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.381370015722773/+0.65420816277382/6.\ 862245e+007/1/112.5 params=1.25/-20/15/-1.23/0/800 float=y maxiter=1300 inside=0 logmap=54 periodicity=10 colors=00010010010010010S100100100100100100C0EH0SE\ 0e90g40j10m00p04r0Cu0Mx0Uz0ez0mz0xz0zz0zz0zz0pz0bz\ 4SzEHzM4zY0zg0zr0zz0zz0zu0ze0u00190K00100000000000\ 0000000600E40PP0Y_0ej0mu0up0zm0zj0ze0zb4z_CzYKz_Hz\ _Ez_Cz_9z_6z_4z_1z_0z_0z_0z_0z_0z_0z_0rb0gb0_b1Pe6\ EeC6eH0eM0gS0gY0gb0gg0jj0mm0pp0pr0rr0uu0xx0xz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz6pgSbMjP4zC0z00z10z\ 40z60z90zC0zE0zH0zK0zM0xP0uS0rU0pY0m_0jb0ge0eg0bj0\ _m0Yp0Ur0Su0Px0Px0Uz0_z0bz1gz9mzHpzMuzUzzbzzjzzrzz\ zzzzzzzzzzzzzzzzzzzzzzzrzzrzzrzzrrxrjpr_jrSerU_rYU\ r_PrbKreErg9rj4rm0rp0rr0ru0ru0rm0re0r_0rS0rM0rE0u9\ 0z10z00mS0ju0jz0mz0mz0pz0pz0rz4rz9uzEuzKuzPxzUxz_z\ zezzjzzpzzuzzzzzzzzzzzzzzzzzzzxzzxzzzzuzzuzzxzzzzz\ zzxzzuzzpzzjzzgzzbzz_zzgzzmzzrzuzzbzzMzz4zz0zz0zz0\ zz0zz0zz0rz9jzMbz_UzmUzpYzpYzrYzu_zu_zx_zxbzzbzzez\ zezzgzzjzzmzzpzzrzzrzzrzz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 22-04-01 (Minibrot with Aura [7]) Date: 21 Apr 2001 22:18:20 -0400 (EDT) Classic FOTD -- April 22, 2001 (Rating 7) Fractal visionaries and enthusiasts: The hazy blue glow surrounding today's tiny Minibrot reminds me of the mystical aura that is sometimes claimed to surround the human body, and is said to be especially brilliant around the heads of saints and holy people. This resemblance inspired the name "Minibrot with Aura". Since I'm not yet in my mystical or philosophical mode, I'll not speculate as to whether such an ethereal glow actually exists around the human body, and can actually be seen by those with extrasensory vision, but if no such thing exists, a lot of hallucinating people or liars are out there. One needs no psychic ability to see the aura in today's image. It was produced by the formula Z^(-1.5)+0.0001*(Z^(-150))+(1/C). The sickle-shaped elements are typical features in the images that result when different portions of high and low powers of Z are combined. After much indecision, I settled on a rating of 7 for today's image, with its soft colors and sharp contrasts. The parameter file renders in a little over 10 minutes on a tired but still functional Pentium 200mhz machine. The GIF image file downloads in a fraction of that time. For those who choose the download, the file may be found on the Web, posted to Paul's site at: and to Scott's site at: But give Paul and Scott an hour or so to post the image. The fractal weather today here at Fractal Central was sunny in the morning and much warmer, but it became cloudy in the afternoon, with a few drops of rain. The temperature of 75F (24C) had the fractal cats in the yard most all day, twitching their ears whenever a drop of rain hit them. As for me, I see that it's time to shut down the fractal shoppe and call it a night. If I can find a trashy enough old sci-fi movie to watch, the day will be complete. If not, I'll watch a Dr. Who show. Until tomorrow or Monday morning, take care, and just because you can't see something doesn't mean that it's not there. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Minibrot_with_Aura { ; time=0:10:18.08--SF5 on a p200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.22503694025169900/+0.092233759045437\ 49/3.857046e+010/1/64.992/-0.026 params=1/-1.5/0.0001/-150/0/300 float=y maxiter=1500 inside=0 logmap=-220 periodicity=10 colors=000A0FA0FA0FA0FA0FA1FA2FA3EA4EA5DA6DA7CA8CA\ 9BAAAABEACAAD6AE2AF3AI4AL5AN6AQ7AT8AV9PYAU`BUbCceD\ hhEmjFq`poZlnYilXekVfiUghTigSkiRmjRokRqlRsmRunRwoR\ yqRzrRzsRzqRzoRzmRzmRzmUznXzo_zpbzqdzJH8JRCGaFCmJ9\ vMCsPEqSHnVJlXMi_OgbRddTbgW_jYYldWbjUToSJuQ9zO0zM4\ vL7rKAnIEjHHfGKbEO_DRXCUUAYR9`O8cL6gI5jF4mC3pF7oHA\ oKEoMHnPKnROnURmWVmZYm``mYZkWYjUXhRWgPVeNUdLTbIRaG\ Q_EPZBOX9NW7MU5LT7OS9RSAURCXRE_RFbQHeQJhQKkPMnPOqP\ PtORwOSzOUzNVzNWzNYzMZzM_zMazLbzLczL`zRYzXVzaSzgPz\ lMzrJzwNzsQzpTzlWziZzfazbdz_gzXjzTmzQpzNozQnzSmzUm\ zXlzZkz`jzcjzeizghzjgzlgznfzqezsezubzs`zqZzoXznVzl\ TzjRziPzgNzeLzcJzbHz`FzZDzYEz_FzaGzcHzdIzfJzhKzjLz\ kMzmNzoOzqOzrRzqUzqWzqZzq`zqczqezphzpjzpmzpozprzpt\ zpIzXWzSizOwzKszNozPkzShzUdzW`zZYz`UzbQzeNzgJzjFzl\ Czn8zq4zs1zu5zr8zoCzmFzjJzgMzeQzbTz_XzY_zVczSfzQhz\ RjzTkzUmzWozXpzZrz_sz`6ze } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 23-04-01 (Swirls [4]) Date: 23 Apr 2001 10:36:06 EDT Classic FOTD -- April 23, 2001 (Rating 4) Fractal visionaries and enthusiasts: Today's fractal rates a 4, though I feel that it has a higher rating in it, which I could develop if I had time to tweak the colors some more. But the FOTD is already as late as it has ever been and I've got a busy day ahead of me, so the image, which I have named "Swirls", will have to stand as it is. The parameter file renders in 2 minutes, making running it as convenient as downloading the completed GIF image. Those who would rather download the image will find the file at: and at: allowing Paul and Scott time to post the file of course. The fractal weather today, (Sunday the 22nd), was like mid-summer, with hot sun and a temperature of 86F (30C), which lured not only the fractal cats, but me also, into the outdoors. This explains today's lateness. That's it for today. Until next time, take care, and be happy. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Swirls { ; time=0:01:50.78--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+4.830750037059846/-2.891827230043619/1\ 126735/1/-35 params=0.01/-100/100/-1.1/-0.95/300 float=y maxiter=400 inside=0 logmap=16 periodicity=10 colors=0000DR7Mc8FQ6GQAHTEIVIJYMJ_QKbULdXLf`MidNkh\ OnlOppPstQuwQwuNrtLmsJhqHdpF_oDVmBRl9Mk7Hj5Di4Gh4J\ h4Mg4Pg3Rf3Uf3Xe3_e2ad2dd2gc2jc2lbBhbJdbRaaZYafVan\ RavO_oLZhIXaFWWCXXGXXJXYMYYPYYTYZWZZZZ_aZ_e__h_`k_\ `n_`qijirtass`sr`tq`tp`up_uo_un_vm_vl_wlZwkZxjZxiZ\ xiZtfXpdVlbTh_RdYQ`WOXTMTRKPPJLMHHKFDID9GCbg5dd6fa\ 7gZ7iW8jU8lR9mO9oLApJArGBsDBuACv8CpEEjJGdOIZTJUYLO\ bNIgOClQ6qS1vT3uR4uQ5uP6tN8tM9tLAsJBsIDsHErFFrEGrD\ JsCLsBNsAPs9Rs9Ts8Wt7Yt6_t6at5ct4et3gt3bp8YmDUmHPm\ MLmRGmVCm_7md3mh6mg9mgCmfFmfImeLmeOmeRmdUndXoc_pcb\ qc`rcZrcfr`mrYgsUbtRXuOSvLMwIHxFByC6z91z64z86z98zB\ BzCDzEFzFIzHKzIMzKPzLRzNTzOWzQYzR_zTazUYzPUzKTzLTz\ LTzMTzMTzNTzNTzNTzOTzOTzPTzPTzPTzQTzQTzRTzRTzRTzST\ zSTzTTzTTzTUzUUzUVzUVzUVzUWzUWzUWzVXzVXzVXzVYzVYzV\ YzVWzUVzTUzSSzSRzRQzQOzQNzPMzOKzOJzNIzMHzLFzLEzKDz\ JBzJAzI9zH9zs9zv9zx9zz8zr } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 24-04-01 (Windmills of Chaos [6]) Date: 23 Apr 2001 21:52:34 EDT Classic FOTD -- April 24, 2001 (Rating 6) Fractal visionaries and enthusiasts: What kind of fractal does the formula Z^0+C or 1+C create? It creates no fractal at all, just an empty circle. What type of fractal then does Z^(0.05)+C create? In this case the empty circle is lopsided, with no evidence of the typical fractal chaos. But take Z^2, subtract Z^0.05 from it, and then add C, and an interesting fractal does appear. I'll not try to describe the indescribable figure, but the oversized thing can be seen by entering the parameters -1, 0.05, 1, 2, 0, 0 into the M-Mix4 formula and letting it iterate. Today's midget lies in a prominent valley on the north side of this fractal. I named the image "Windmills of Chaos" when I noticed that the four open spirals toward the corners vaguely resemble windmill blades. And of course the chaos is there as always, lying in vaguely organized form all through the picture. With a render time of just under 5 minutes, running the parameter file is a bit annoying. A better choice is to give Paul and Scott a chance to post the GIF file of the image to their web sites at: and at: and download the image from there. The fractal weather today was very summer-like. In fact the temperature of 90F (32C) felt a bit too warm. The fractal cats enjoyed the warmth however, as they stretched to their full cat-lengths on the porch most of the afternoon. As for me, I'm about finished for the day. It's been another busy one, but I'll be here again tomorrow, with more fractal goodies. Until then, take care, and be at ease. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Windmills_of_Chaos { ; time=0:04:45.45--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.64915135165492830/-0.619948053295606\ 6/1320520/1/-134.999 params=-1/0.05/1/2/0/0 float=y maxiter=500 inside=0 logmap=78 periodicity=10 colors=000d1gd1ge2hf3ig4jh5ki6li7lh8if8dd8`b9W`9SZ\ ANXAJVAETBARB5PB1V9F_7Td9fi6tjNokSklXgk_`hZZdXV`UR\ WQMSNIOJEJG9FC5B91CB2CC2DD3DE3EF3EG4FH4FJ5GK5GL5HM\ 6HN6KO7PP7UQ7ZOAcNChLEmPHrUJvZLzaNwZOrUPmPQhNRcPSa\ QSXTYTWbPZgKalGdqCgvDhsDhpDimDijDigEjdEjaEkZEkWEmT\ FrQFwNFzKFwHFsFHoMIkSJjZKidLhkMgqNgwPisQjoRlkSmhUo\ dVp`WrXXsUVoXTkZSgaQccO_fNWhLSkJOmIKpGGrECuD9wCCuC\ EtBHrBJqBMpAOnARmATl9Wj9Yi9_hI`PO`9QbFSdLUeRVgWXia\ Zjg`lmamrdkpfjohimjgllfjneimbol`tkZyi_uh`qg`mfajeb\ fcbbbc_acW`dS_ePYeLXfHWgEVgAUh6Th3WaCZWL`PTcJafCjh\ 6rf8seAsdCscEsaGs`Is_KsZMsXOsWQsVSsUTsXVpZWm`YjbZh\ d_efabhb`jcYleVnfSpgQriNtjKvkIicUXWeKOpQJhWFaaBVf7\ Od8Rb8T`9VZ9XXA_VAaTAcRBePBhNCjLClKCnIFhHHcGKZFMTE\ PODRJCUDBW8AY3FZ2J_2N`2Ra2Vb2Zc1be1fg1ji1nk1jm8goE\ dqKarQZsWWtaTugQvmNwsKxyNyuPzqRznTzjVzfXzc_z`azXcz\ TezPgzLizIdzG_zFqzKpzKpzK } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Edward Barton" Subject: Re: (fractint) C-FOTD Date: 24 Apr 2001 11:34:08 +0200 Jim Muth, Throughout the short time I have been part of this discussion list, I have noticed that in your FOTDs, you continually state that a faster rendering speeds are to be searched for, even if that means getting a new computer. I don't mean to sound like I am criticising you, but I ask you to remember what the waiting time was when fractals were discovered, as well as the quality of the resulting image, and remember that the more interesting fractal images are those which are hidden deep inside the pattern of a fractal, and so take significantly longer to render. Edward Barton BTW: Despite the tradition of waiting for a week for a fractal, I do so wish that I didn't have to. I use my Pentium 133 for other things as well, and during the rendering, I can do nothing. _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) Re: C-FOTD Date: 24 Apr 2001 09:31:04 -0400 (EDT) At 11:34 AM 4/24/01 +0200, you wrote: >Jim Muth, >Throughout the short time I have been part of this discussion list, I have >noticed that in your FOTDs, you continually state that a faster rendering >speeds are to be searched for, even if that means getting a new computer. When one is working with fractals, it is obvious that CPU speed is important. I do not need to state the fact. When I do state it, I am merely repeating the obvious. I have no memory of stating that one should go out and spend money they cannot afford on a new computer, though I suppose it could be implied in my words. >I don't mean to sound like I am criticising you, Your post reads more like a letter of frustration than one of criticism. >but I ask you to remember >what the waiting time was when fractals were discovered, as well as the >quality of the resulting image, I was there, and I remember well the overnight waits to see a fractal that we now see in a few minutes. >and remember that the more interesting >fractal images are those which are hidden deep inside the pattern of a >fractal, and so take significantly longer to render. True! This is where I search for my FOTD's. >Edward Barton > >BTW: Despite the tradition of waiting for a week for a fractal, I do so wish >that I didn't have to. I use my Pentium 133 for other things as well, and >during the rendering, I can do nothing. Yes, sometimes the wait does become annoying. FOTD coming in 15 hours. Jim Muth Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: O Bd Subject: (fractint) Targa Output Date: 24 Apr 2001 13:39:04 -0400 (EDT) Hi! I've been trying to get a Targa output file but the file seems to be created in the wrong format. Instead of an image I get one that's sort of looking like a slinky!!! Is there a way to fix this? Or am I using the wrong version? Im using 19.2 Any help will be appreciated. Thanks O Bd. The No.1 Utah Jazz fan in England ______________________________________________ FREE Personalized Email at Mail.com Sign up at http://www.mail.com/?sr=signup Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) Targa Output Date: 24 Apr 2001 14:16:26 -0500 O Bd wrote: > > Hi! I've been trying to get a Targa output > file but the file seems to be created in > the wrong format. Instead of an image I get > one that's sort of looking like a slinky!!! > Is there a way to fix this? Are you trying to do 3-D transforms?? And are you doing any Overlays?? Have you set any of the Light Source Parameters?? > > Or am I using the wrong version? Im using 19.2 The most current version being developed is 20.1.07 and may be acquired from the Development Team's web site: http://www.fractint.org/ But the latest released version of Fractint is 20.0 and is available from the Spanky Fractal Database location: http://spanky.triumf.ca/www/fractint/fractint.html > > Any help will be appreciated. What program are you using to open the Targa file that was created?? Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Targa Output Date: 24 Apr 2001 20:07:33 -0500 > But the latest released version of Fractint is 20.0 and is available > from the Spanky Fractal Database location: I believe you will find that the Targa output was broken in version 20.0. It's been fixed in the developer's version. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) Targa Output Date: 24 Apr 2001 23:11:51 -0500 Jonathan Osuch wrote: > > I believe you will find that the Targa > output was broken in version 20.0. > It's been fixed in the developer's version. > Yes, I knew some Patches had been applied, just did not go through all of the notes to see exactly what version/release/mod-level the repairs were made at. Hopefully "O Bd" will choose to upgrade from the 19.2 level that is being used by him/her, and use the 20.1.07 level. And maybe do some further testing for you guys within the area of Targa files. Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Date: 25 Apr 2001 11:51:43 -0000 >From: "Paul N. Lee" >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) >Date: Thu, 19 Apr 2001 00:16:05 -0500 > >Andrew Coppin wrote: > > > > Thankyou paul. > >Just thought credit should be mentioned where due. :-) > > > > > It seems only fair to mention that I had > > help from others on this list thought... > > (Wish I could remember whom, but I definitly > > had help!) > >You first started discussing the "Branch Cuts" on Fri, 07 Apr 2000. And >some of the individuals involved with that topic on the List were as >follows: > > Barry N. Merenoff (Collin Merenoff) > Morgan L. Owens > Tim Wegner > Jim Muth > Kenneth Childress > Damien M. Jones > >This went on until Tue, 18 Apr 2000. I am sure that the archives will >show the details of who did what. Just spend an hour trolling through the FractInt archives. Gee! I really must do this more often!!! The archives show that Morgan provided his usuall deep insights, and Jim produced a couple of top-notch FotDs with the resulting formula, but the formula itself basically came from Mr. Merenoff (with a type-error correction form Kenneth). Basically, I posted a formula that was partially broken, thus: >From: "Andrew Coppin" >Subject: (fractint) Branch Cuts >Date: 10 Apr 2000 10:22:48 GMT > >So log(Z) is a cork screw, and you have to take a 360 degree slice of >it. >Hmmm... This formula (I think) varies the slice taken, but only by >another >360 degrees. If k is below -3 then you get what the formula parser > >normally does. If you now raise k, you get a nice branch cut shift... >until you >reach +3, and thereafter there is no further change. Any ideas >how to >correct this? > >--BEGIN >comment >{ > Andrew Orphi Coppin, 10 May 2000AD >} > >BrotBC = { ; Z^2.5 + C > ; real(p1) = phase shift. > > p = real(p1) > Z = C = Pixel: > Z = log(Z) > IF(imag(Z) > p) Z = Z + flip(2*PI) ENDIF > Z = exp(2.5*Z) + C > |Z| < 4 >} >--END Later that day, the following message appeared: >From: Barry N Merenoff <110144.2274@compuserve.com> >Subject: (fractint) Branch Cuts >Date: 10 Apr 2000 08:31:09 -0400 > >Andrew, try this: > >p=3Dreal(p1)+PI >q=3D2*PI*floor(p/(2*PI)) >r=3Dreal(p1)-q >Z=3DC=3DPixel: >Z=3Dlog(Z) >IF(imag(Z)>p) Z=3DZ+flip(2*PI) ENDIF >Z=3Dexp(2.5*(Z+flip(q)))+C >|Z|<4 >} > >Note: I don't know if Fractint has a floor function, but it should >have >something equivalent to it. > >Sincerely, > Collin Merenoff As said, the formula was corrected (the "IF(imag(Z)>p)" should actually be "IF(imag(z)>r)"). And then I posted the message Paul quoted, which is basically the same but with different variable names. (But still, Jim posted half a dozen FotDs with my name on 'em. And why not? I *thought* of it!) Interestingly, the archive also shows that this is the thread that eventually lead to the addition of extra .FRM parameters in a developer's patch (can't remember which number tho). Also during this period there was some cool descussion on why the Mandelbrot set pops up everywhere. And I asked if fractint's parser could have an arg() function added. (It never happened!) There was some talk from Tim about making movable branch-cuts an integral feature of fractint (which also never happened). Thanks. Andrew. PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"? _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 25-04-01 (OOOF! [3]) Date: 25 Apr 2001 09:20:35 EDT Classic FOTD -- April 25, 2001 (Rating 3) Fractal visionaries and enthusiasts: Yes, I'm late again today with the FOTD. It's getting to be a habit. My excuse is the same old one which needs no repetition. Today's fractal image, which looks like a rotten melon with a face drawn on it, being squashed, fairly cries "OOOF!". So this is what I named it. Normally, I avoid images that resemble funny faces, but today's picture is so ridiculous that I had no choice but to declare it FOTD for April 25. I displayed my disgust with comedy fractals by rating the image a lowly 3. The formula behind the image is Z^2+C -- the Mandelbrot formula. The mouth of the squashed melon-head is actually a Mandel-midget on the tip of the longest northwest filament shooting out from the fifth bud along the negative tail of the M-set. The midget is so distorted because it has been sliced in a different direction through the 4-dimensional Julibrot, which is the assemblage of all Julia sets and all perturbed Mandelbrot sets. Though the Mandelbrot formula drew the image, the image is not part of any Mandelbrot set. Nor is it part of any Julia set. It is kind of a hybrid, with both Mandelbrot and Julia characteristics, and a few entirely new characteristics, such as the stretching effect, thrown in for extra measure. I seem to have forgotten the Julibrot and the fourth dimension since becoming involved with the M-Mix4 formula and its limitless variety of midgets. But perhaps it's time to get back to basics as well as the unknown, and nothing is more unknown than the fourth dimension. Since the FOTD is so,late, the parameter file is the fastest in many months, rendering in less than a minute on a 200mhz Pentium. It will take longer than that to reach the GIF image, which is posted to: and to: The fractal weather was very warm again today. The cats, comfort seekers that they are, took full advantage of the 86F (30C) temperature, by spending the entire afternoon lounging in the yard. That's it for today. It's time to rev up the fractal shoppe and get busy with other things. Until next time, take care, and life is never so good that it can't get better. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ OOOF { ; time=0:00:54.58--SF5 on a p200 reset=2001 type=formula formulafile=multirot.frm formulaname=multirot-xz-yw passes=b center-mag=-0.00000000002107355/-0.000000000029447\ 31/8.638531e+009/14.687/-180/35.229 params=45/45/-1.4041038040019/0.00422258114480\ 08/-1.4041038040019/0.0042225811448008 float=y maxiter=600 inside=255 logmap=147 periodicity=10 colors=000Eg`JgbOgdSgfXgh`gjeglignfijckg`ldYnaVpYS\ qVPsSMtPVrJbpD_rFXsGUtIRvJOwLMxMKpQIiTGaXFV_DNbBGf\ 98i81lYQN`UQbYTdaWgdZihakldmogelgZjgShgLfgEdg7bg0`\ gFcMTf091V74X67Z5A`4Db3Gd2Jf1MgJaYDaP7aG1a7TF6UO9U\ WBUdEUlGUtIQjTM`bIRmFIwNLqVNlbQfjSaqUXpSVpRTpPRpOP\ pNOjLLeJI`HFWFCQD9LB6G93B7195Y9ak8Vj7Pj6Ji6DiCKcHQ\ YNWTSaNXgIfbVoYgxUskdr_nrcgkfaeiW_lPUoJOrDIu7CkCQa\ GcbLebQfcVhcZidckdhlemneqofiofaogUogMogFoaLmWQkRVj\ L_hGdgI`cLY_NUWQQRSNNVJJXGFaJZfLrZLqRLpKLoMQpNVpO_\ pPdpQipRnpSspWrkZqfbpaepYioTlnOpmJsmFklJckNXkQPjUH\ iYAi`QfdddgsbjVac6`X5_S5_N5ZI4ZD4Y84Y3BVIHSXOPkUNz\ ZRsbUlfXej_ZnbSteEzh1daqUysYwmauhesbhqYloTpmNtkIwj\ DsbBpV9mO8iG6f84c13kPrmRlnSgpTaqUXsWStXMvYHwZCuVBt\ RAsN9rJ8qF7pB6o85k58h2Ae0CaBPZM`WXlaThgPdmM`sIXxFU\ ZPM9ZEAaFAcFBeGBgGCfEDeDEeBFdAGd8Hc7Ic6HZ7HV7GR76h\ l4ilGcdRYYaSQlMJwHCgQL000 } frm:multirot-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p2, c=e*imag(pixel)+p3: z=sqr(z)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) C-FOTD 26-04-01 (Baubles [6]) Date: 26 Apr 2001 00:40:06 EDT Classic FOTD -- April 26, 2001 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal formula takes Z^(-11.5), adds 4 times as much Z^(-1.15), then adds the reciprocal of C. Adding 1/C instead of the usual C turns a fractal inside-out. The Mandelbrot set, instead of appearing as a lake in an infinite continent, appears as an island in an infinite lake. But fractals created by negative powers of Z normally appear as islands in infinite lakes, so turning these fractals inside-out changes them into lakes surrounded by infinite continents. Combining two different negative powers of Z in an inside-out fractal and initializing Z to a critical value produces a fractal with quadratic midgets. This is the type of fractal that is the parent of today's scene. This parent fractal is a huge thing filled with circular features resembling zippers, with a size exceeding even the full outzoom capability of the Fractint program. Today's midget lies in an area rich with these zipper-circles. I named the image "Baubles". The name came to mind after I spent 1/2 hour with the image on the screen, doing other tasks and thinking of nothing better. I rated the image an above- average 6. The parameter file renders in under 6 minutes, which is slow enough to make a download of the GIF image file the better choice. That download will ba available within the hour at: and at: The fractal weather today here at Fractal central was cloudy and much cooler than yesterday. The temperature of 52F (11C) was just cool enough to keep the fractal cats confined to their windows, where they sit to watch the outside when they can't actually be out there. It's now time to call it a night. . . It's a night! . . . Until next time, which, within an accuracy of 67 percent, will arrive in 24 hours, take care, and life as well as cats are better with fractals. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Baubles { ; time=0:05:53.56--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=456.568/-70.8747/1.353355/1/132.499 params=1/-11.5/4/-1.15/0/300 float=y maxiter=1200 inside=0 logmap=55 periodicity=0 colors=00020K30N60S80V90YA0bD0eE0kG0oH0tN6vSCwYHyb\ NzgUzmYzrbzwgzzkzymzzvzztzptyerwVrtKppAoo0kk0jj0gg\ 2ce8bcD``H__NYYUXV_XUeVSjUPpSNwQMzPJzNHzNGzPMzPQzP\ XzP`zPgwPkvPprSkpVhoYem`bjc_heXghUekQboN`rK_tHYwEV\ zCUz9Sz6Qz3Pz2Pv0Po0Pj0Nc0NY0NS0NN0QMPNQUMVXK_`Jcc\ HhhGmkErpDwtCzyAzz9zz8zzEzzKzzSzzYvzcrzkmzrhzzczz_\ zzXzz`zzewzjozogzt_zwSzzKzzDzz6zz0zz0zz0yz0pz0gz0_\ z0Qz0Jz0Az03z00z00z00z00z00z00z00z20z50z80z90zH0zP\ 5wXAreGomMjvQgzY_weUpmMjvGczA_tGXkMUcSQXYNPcKHjJKg\ GNcEQbCU_AXX9_V6`S5cQ2gN0jK0mJ0pG0rE0tD0vC0vA0w90w\ 80y60y50z30z20z00z00w02r06o0Aj0Ge0Kb0PY0VV0_Q2cM2j\ J2oE2tA2z82z32z02zEHvUXchkNyz8zz0zz0zz0zz2zz5zz8zz\ AwzDvzGrzJpzMmzPkzSUzbDzm0zy0zz8zcXzAwz0kz0bz0Sz0J\ z0Hz8HzHGzUGzcDz`Az_8zY6zXAzUEzQHzPMzMQzJUzHYzEbzC\ ezAjz8oz5rz3wz0zz0vz5rzAozGjzMgzSczXezUgzSgzPhzNhz\ KjzJjzHkzEmzDmzAoz9oz6pz5 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: (fractint) Web Based Archives Date: 26 Apr 2001 14:31:24 -0500 Greetings, This information is for those that do not know how to use the Usenet Newsgroups or may have problems using them. Since some of the other web based Usenet Newsgroup Archives are either no longer available or not functioning (such as NailNews), another one has become available: ETIN Technologies Chronologically relevant searching of messages. Browsing of text and binary newsgroups. Posting available. Free, Public, Complete, and Anonymous. Text messages are archived and retained permanently. Binaries are retained 10 to 20 days. Here are the direct URLs for fractal related NGs: A.B.P.F. http://www.etin.com/?folder=alt%2Ebinaries%2Epictures%2Efractals A.F.P. http://www.etin.com/?folder=alt%2Efractals%2Epictures A.F. http://www.etin.com/?folder=alt%2Efractals S.F. http://www.etin.com/?folder=sci%2Efractals A.B.F-A. (this one is not available) Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Rupert Millard" Subject: (fractint) Sinusoidal gradient maker Date: 27 Apr 2001 07:40:42 -0000 Hello everybody! It seems that Polynomial gradient maker was a bit boring for you colourful lot - So I've made Sinusoidal gradient maker. This program is the same as polynomial gradient maker, except that it puts sine waves in the red, green and blue channels, instead of polynomials. You can see the page and donwload the program at: http://www.geocities.com/kangarupert/sinu_grad_maker.html From, Rupert _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Thierry B." Subject: Re: (fractint) Sinusoidal gradient maker Date: 27 Apr 2001 08:03:58 +0000 Rupert Millard wrote: > > > This program is the same as polynomial gradient maker, except that it puts > sine waves in the red, green and blue channels, instead of polynomials. > > You can see the page and donwload the program at: > http://www.geocities.com/kangarupert/sinu_grad_maker.html > Same thing, but in fortran with a web interface http://la.buvette.org/fractales/palette.html Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 27-04-01 (Object Around Midget [5]) Date: 27 Apr 2001 08:29:52 -0400 (EDT) Classic FOTD -- April 27, 2001 (Rating 5) Fractal visionaries and enthusiasts: As I pondered today's image, I was reminded of nothing in particular. The decorations around the midget do resemble several computer animations I have seen. And they sometimes impressed me as the tentacles of some fantastic monster lurking on the sea floor. But all these impressions are so vague that I named the image with the very simple and non-descriptive name, "Object Around Midget". The MandelbrotBC formula is responsible for the image, which is part of the infinite Z^(sqrt2)+C fractal. This fractal is my most frequently explored with an exponent of Z between 1 and 2 because in this fractal the midgets are easier to find than in most fractals lying in this exponent range. Confining explorations to the fractal created by only one exponent between 1 and 2 is not limiting, since when drawn by the MandelbrotBC formula, the fractal is infinite in surface extent as well as depth and variety. On my 200mhz Pentium the image takes almost 3/4 of an hour to render. It will therefore be an hour or so before it is available on the Web at: and at: The fractal weather today (actually yesterday, April 26) was just about average for this location at this time of year, with warm sun and a temperature of 65F (18C). These conditions had the fractal cats in the yard most of the afternoon, acting like kittens. Such behavior is most undignified for cats of their venerable age of 9 years. As for me, it's past 8:15am, and I've got a busy day before me. So until next time, take care, and enjoy the flowers of Spring of the leaves of Autumn. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ ObjectAroundMidget { ; time=0:43:53.22--SF5 on a P200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.15\ 578257934389980/+1.535940899307265/4.223478e+008/1\ /12.5 params=1.414213562373/0/0/0 float=y maxiter=6000 inside=0 logmap=-1150 periodicity=10 colors=000SaZOfUHiRDnM8qJ2vE0yB0x80rZ0mU0hP0cM1`H4\ YE8ZADd6Hi2Mp0Pt0Op0Ml0Ki0Jf0Ha0GZ0EW0DS0BP0MfOXvn\ RkiK`dEP`AEX44S00O00K00J00H00G00E04D08B1DA2G82K74P\ 66U46X47`G8aR8ccAdnBfzBhzD`zDSqEKhEEZG7PG0GG07K0EO\ 4KRARUEXXKc`PicWpf`vdkzcvzazz`zzXzzWzzSzzRzzOzzMxz\ KuxHqvGnsDkqBhnAflRWhhKdnAhu0ky0nx0ix0fx4ax7ZxBUxG\ RxKMxOJxSExXBx`8vXDvUGvRKuPOuMSuJWsG`sEcsBhq8kq6pq\ 4sp1xp0zp0zp0zzK`zOZzRZzUXzXXz`WzcWxfUviUslUppSnsS\ kvRhyRfzPczPazPazUZzSXzRWzPSzORzMPzMOzKKzJJyHHyGGy\ GRlJ``MiOPsBSz0Wz0Zp6hWMpBcx0uz0qz0py0nx2mu4msAmnG\ mkMmhRmdXmacmXhmUnmRumOymKcmnJmzMmzOmzPmzSmzUmzWmz\ Zmz`mzamzdnzfqzhuzixz0zD0zE4zGBzHJzHRzJZzKfzMnzMqz\ PuzSxzUzzXzzZzzazzcXz0az0dz0hz0kz0nz0qz0uz0xz0sz0n\ z0iz0dz0az0Xz0Sz0Oz0Jz0Gz0Bz07z02z00z01zG1zX2zn2zz\ 1zv0zl0zc0zW0zM0zD0z40z00z06z2Bz6Hz8OzBUzEazHhzKnz\ OuzRzzUzzX7z0Bz4hziczfZza } frm:MandelbrotBC { ; Inspired by Andrew Coppin e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Date: 28 Apr 2001 17:07:15 +1200 At 23:51 25/04/2001, Andrew Coppin wrote: >PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"? One of the hassles involved with many functions is that they are many- valued (and hence, strictly speaking, not functions at all). Even the humble square root is guilty of this - z^(1/2) usually has two values. And as for log(z), or arcsin(z)... What would be nice is if there were some way of turning these many- valued functions into single-valued functions. Bermhard Riemann came up with a geometrical stunt that did just this by replacing the complex plane with a suitable generalisation (mathematicians just loooove to generalise things). His idea was to separate each value of the function by placing it on a separate "sheet", which on its own looks like an entire complex plane. For example, if the values of z^(1/2) for a given z were a_z and -a_z, then a_z would go on one sheet and -a_z would go on another. Then you could take one sheet and say that the values on it are _the_ values of the function. To drop down into real arithmetic for a second, this is analogous to saying that _the_ values of the square root function are the nonnegative ones. A function may require more than one sheet. The log(z) function, as immortalised in the MandelbrotBC formula, has an infinite number of sheets, since log(z) usually produces an infinite number of values for a given z (if w is one such value, then so are w+2pi, w+4pi, w+6pi..., among others). But of course there is more to it than just slapping down extra layers on the complex plane like tracing paper. For a start, there are often points where the sheets merge (such as the point z=0 for the function z^(1/2)). Also significant is the question of where the function moves from one sheet to another. After all, if this is supposed to be a nice continuous function, you don't want to introduce a nasty discontinuous artefact by suddenly jumping from one sheet to another. So you want to stitch all these sheets together in some way into a single continuous surface, and it is exactly this that Riemann described. Let's take the log function as an example, mainly because that way the MandelbrotBC formula is available to play with. The log function goes blecchh at z=0, so we'll stick with nonzero complex numbers. As I said, if log(z)=w, then log(z)=w+2npi, for any integer n. So w and w+2pi, w+4pi, w-2pi, w-4pi, w+158pi, ... are all on separate sheets (which we can index by n, if we are so inclined). The surface is sort of helical. We start on the ground floor (n=0), and we can walk around the origin until we've made a complete circle, whereupon we find ourselves on the first floor (n=1). Another complete circle and we're on the second floor (n=2). Going the other way from the ground floor we find ourselves on the first basement level (n=-1), then the second basement (n=-2), and so on in that direction. But where precisely do we change floors? What the Riemann surface shows is that such a question is more a matter of convention than anything to do with the property of the log() function itself. We could draw a line out along the positive real axis (on each sheet) and say "Here is where we change sheets", but we could just as easily draw it along the negative real axis, or either imaginary axis or anything in between. Wherever you place it, you can extract a sheet out of the surface that covers the entire complex plane (except of course for the origin) by cutting along your chosen axis on any sheet and an adjacent sheet. It should be pretty obvious that these lines I've been talking about are the branch cuts. Conventionally, the log() function is cut along the negative real axis. So is the square root function, for that matter, while the arctangent function is cut along the negative imaginary axis starting at 0-i and extending downwards towards -infinity. To provide a bit of a summary, I'll describe the Riemann surface of the z^(1/2) function. Since this function is at most two-valued (the only exception being of course z=0, which has one value), the Riemann surface is made by stitching two sheets together. Laying them atop each other, we see that they have to actually meet at z=0 (because they have the same value there). Now, what do the two values of z^(1/2) have in common? They're negations of each other, of course, which on the complex plane is equivalent to rotation about the origin of 180 degrees (or more appropriately, pi radians). So if we were to start at one value and walk around the origin and arrive back at our starting point, we'd find ourselves on the other sheet. Another walk around and we really will be back where we started. We can manage this by cutting the sheets as follows. Starting at the origin, we cut a slit out to infinity (conventionally as I mentioned above), join the lower edge of the lower sheet to the upper edge of the upper sheet, and the upper edge of the lower sheet to the lower edge of the upper sheet. Don't worry if this violates your three-dimensional imagery - it's not a stunt that can be pulled off in 3D without the optical illusion of the two sheets apparently interpenetrating. And there's the surface. The (illusory) crossover line along the axis can be waved and wiggled about all over the complex plane - as long as one end remains rooted at the origin - and every such wave and wiggle can be used to define a branch cut for separating the surface back into sheets again. Its precisely the positioning of the branch cut for the log() function that is explored by the MandelbrotBC formula. If you build an animation where you steadily increase the branch cut parameter, you can almost see the spiral staircase effect as you climb higher and higher. See also:http://library.wolfram.com/examples/riemannsurface/ Morgan L. Owens "I _had_ to ask..." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 28-04-01 (Semi-Chaos [4]) Date: 28 Apr 2001 08:39:43 -0400 (EDT) Classic FOTD -- April 28, 2001 (Rating 4) Fractal visionaries and enthusiasts: Today's image is of a type that I rather enjoy exploring -- chaotic, yet filled with just enough patches of order and theme-sections to make it interesting. I named the image "Semi-Chaos" mostly as a description. The midget in today's image is of the order 1.618..., and, for a change, is not at the dead center of the frame. Actually, the midget is an added attraction, the main interest lying in the fragmentary elements scattered throughout the scene. Since I find only minor artistic merit in the image, and only a modicum of math interest, I could rate it no higher than a 4. But it's still worth a look, if only to see what a Z^1.618+C Mandeloid midget looks like. The MandelbrotBC formula, which is rather a committee project, once again did the work of rendering the image. The render was completed in 13-1/2 minutes on a 200mhz Pentium. The GIF image, already rendered, will soon be available on the Web at: and at: The all-important fractal weather was quite pleasant today. The cats approved of the warm sunshine and temperature of 77F (25C), and showed their approval by sleeping on the porch most of the afternoon. While searching this evening for today's fractal, my mind drifted into heavy philosophical speculation, and I pondered about gravity and dark matter. The problem is that the outer parts of the galaxies are rotating too fast to be caused by the gravity created by the visible matter of the galaxies. To account for this discrepancy, astronomers have hypothesized that the galaxies are filled with large amounts of undetectable material they have named dark matter, and this unseen material is causing the excess gravitational acceleration. But this explanation is not satisfactory, since if the matter cannot be detected, it will be most difficult if not impossible to confirm its existence. There may be another possible way of accounting for the excess rotational velocity, and this is to assume that, like so many other natural phenomena, the Newtonian law of gravity is valid only within a limited range, which includes our scale of experience in everyday life, as well as the solar system. But perhaps, beyond this scale, gravity is quantized, and there is a minimum possible gravitational acceleration. If this is the case, then the outer parts of the galaxies would be subject to this minimum acceleration, which, being greater than the Newtonian laws of gravity would produce, would cause the excess velocities observed in the outer parts of the galaxies. I'll not speculate on how this might affect the ultimate fate of the universe. Since this alternate explanation is so obvious, it must have already been thought of by many astronomers, and probably discarded because it contains a fatal flaw. But it did supply me an hour or so of diversion while working on a dull routine job. Perhaps I'll continue this line of speculation on the philofractal list in the next FOTD. I now see that it's post time, so until tomorrow, take care, and could the big bang turn into a big bust? Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Semi-Chaos { ; time=0:13:37.34--SF5 on a P200 reset=2001 type=formula formulafile=semikaos.par formulaname=MandelbrotBC passes=1 center-mag=-0.501937/-0.59952/582.5136/1/49.999 params=1.618034/0/122/0 float=y maxiter=30000 inside=0 logmap=145 periodicity=10 colors=00050U4DU2DU0FU0FU00U05U0AU0Fc5KmCPpKVnR_kY\ didiekndss`zy_zzWzzVzzSzzPzzNzzMzwKzsIzpHzlFzgCwdA\ u`9qY7pS5lP4kM2gH0eD0bA0`70Y20W00S00P00R00R00R00R0\ 0R00R00R00R00R00R00R00R00R00R00R00S00S00S00S00S00S\ 00S00S00S00S00S20S20S20S22S42S42V44V44V44V55V55V55\ V57V77V77V79V79V99V9AV9AV9AW44V57V79V9AV9CSADSCFSD\ HSDISFKRHNRHPRIRRKSRMVPMWPNYPP_PR`PRbNSeNVgNYiN`kN\ dlMgnMipMkqMls_qseuu`quYnuWguN`wP`wP_wP_wR_wRYyRYy\ SYySWySWyVWzVVzVVzWVzWSzWSzYSzYRzYRz_Rz_Pz_Pz`Pz`P\ z`NzbNzbNzbMzdMzdMzdKzeKzeKzeIzgIzgIzgHziHziHziFzk\ FzkFzkDzlDzlDzlCznCznCznAzpAzpAzs7zq9zqAzsCzsDzsFz\ sHzuIyuKuuMqwNpwPlwRiySeyVbyW`zYYz_Vz`Rz_Kz`MzbNzb\ PzdRzeSzeVzgVziWziYzk_zk`zlbzndzndzpezqgzqizskzslz\ unzwnzwpzyqzzszzuzzwzzwzzszzpzzlzzkzzizzgzzgzzgzzg\ zzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzz\ gzzgzzgzzgzzgzzgzzgzzgzzg } frm:MandelbrotBC { ; Formula by Andrew Coppin e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) Re: C-FOTD 18-04-01 Date: 28 Apr 2001 08:45:26 -0400 (EDT) At 05:07 PM 4/28/01 +1200, Morgan Owens wrote: >At 23:51 25/04/2001, Andrew Coppin wrote: > >>PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"? Great explanation Morgan! This is the first time I've actually understood exactly what the branch-cut discontinuities are. Jim M. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: DeBow Freed Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Date: 28 Apr 2001 08:17:02 -0500 Cheers to Morgan from the peanut gallery, too. "Morgan L. Owens" wrote: > At 23:51 25/04/2001, Andrew Coppin wrote: > > >PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"? > > One of the hassles involved with many functions is that they are many- > valued (and hence, strictly speaking, not functions at all). Even the > humble square root is guilty of this - z^(1/2) usually has two values. > And as for log(z), or arcsin(z)... > > What would be nice is if there were some way of turning these many- > valued functions into single-valued functions. Bermhard Riemann came up > with a geometrical stunt that did just this by replacing the complex > plane with a suitable generalisation (mathematicians just loooove to > generalise things). > > His idea was to separate each value of the function by placing it on a > separate "sheet", which on its own looks like an entire complex plane. > For example, if the values of z^(1/2) for a given z were a_z and -a_z, > then a_z would go on one sheet and -a_z would go on another. Then you > could take one sheet and say that the values on it are _the_ values of > the function. To drop down into real arithmetic for a second, this is > analogous to saying that _the_ values of the square root function are > the nonnegative ones. > > A function may require more than one sheet. The log(z) function, as > immortalised in the MandelbrotBC formula, has an infinite number of > sheets, since log(z) usually produces an infinite number of values for a > given z (if w is one such value, then so are w+2pi, w+4pi, w+6pi..., > among others). > > But of course there is more to it than just slapping down extra layers > on the complex plane like tracing paper. For a start, there are often > points where the sheets merge (such as the point z=0 for the function > z^(1/2)). Also significant is the question of where the function moves > from one sheet to another. After all, if this is supposed to be a nice > continuous function, you don't want to introduce a nasty discontinuous > artefact by suddenly jumping from one sheet to another. > > So you want to stitch all these sheets together in some way into a > single continuous surface, and it is exactly this that Riemann > described. > > Let's take the log function as an example, mainly because that way the > MandelbrotBC formula is available to play with. The log function goes > blecchh at z=0, so we'll stick with nonzero complex numbers. As I said, > if log(z)=w, then log(z)=w+2npi, for any integer n. So w and w+2pi, > w+4pi, w-2pi, w-4pi, w+158pi, ... are all on separate sheets (which we > can index by n, if we are so inclined). The surface is sort of helical. > We start on the ground floor (n=0), and we can walk around the origin > until we've made a complete circle, whereupon we find ourselves on the > first floor (n=1). Another complete circle and we're on the second floor > (n=2). Going the other way from the ground floor we find ourselves on > the first basement level (n=-1), then the second basement (n=-2), and so > on in that direction. > > But where precisely do we change floors? What the Riemann surface shows > is that such a question is more a matter of convention than anything to > do with the property of the log() function itself. We could draw a line > out along the positive real axis (on each sheet) and say "Here is where > we change sheets", but we could just as easily draw it along the negative > real axis, or either imaginary axis or anything in between. Wherever you > place it, you can extract a sheet out of the surface that covers the > entire complex plane (except of course for the origin) by cutting along > your chosen axis on any sheet and an adjacent sheet. > > It should be pretty obvious that these lines I've been talking about are > the branch cuts. Conventionally, the log() function is cut along the > negative real axis. So is the square root function, for that matter, > while the arctangent function is cut along the negative imaginary axis > starting at 0-i and extending downwards towards -infinity. > > To provide a bit of a summary, I'll describe the Riemann surface of the > z^(1/2) function. Since this function is at most two-valued (the only > exception being of course z=0, which has one value), the Riemann surface > is made by stitching two sheets together. Laying them atop each other, > we see that they have to actually meet at z=0 (because they have the > same value there). Now, what do the two values of z^(1/2) have in > common? They're negations of each other, of course, which on the complex > plane is equivalent to rotation about the origin of 180 degrees (or > more appropriately, pi radians). So if we were to start at one value and > walk around the origin and arrive back at our starting point, we'd > find ourselves on the other sheet. Another walk around and we really > will be back where we started. We can manage this by cutting the sheets > as follows. Starting at the origin, we cut a slit out to infinity > (conventionally as I mentioned above), join the lower edge of the lower > sheet to the upper edge of the upper sheet, and the upper edge of the > lower sheet to the lower edge of the upper sheet. Don't worry if this > violates your three-dimensional imagery - it's not a stunt that can be > pulled off in 3D without the optical illusion of the two sheets > apparently interpenetrating. And there's the surface. The (illusory) > crossover line along the axis can be waved and wiggled about all over > the complex plane - as long as one end remains rooted at the origin - > and every such wave and wiggle can be used to define a branch cut for > separating the surface back into sheets again. > > Its precisely the positioning of the branch cut for the log() function > that is explored by the MandelbrotBC formula. If you build an animation > where you steadily increase the branch cut parameter, you can almost see > the spiral staircase effect as you climb higher and higher. > > See also:http://library.wolfram.com/examples/riemannsurface/ > > Morgan L. Owens > "I _had_ to ask..." > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 29-04-01 (Veil-Nebula [6]) Date: 28 Apr 2001 21:32:04 -0400 (EDT) Classic FOTD -- April 29, 2001 (Rating 6) Fractal visionaries and enthusiasts: In the constellation of Cygnus, which is directly overhead in the summer months at a latitude of 39N, there is a delicate nebula, the remnants of a supernova explosion that took place some 25,000 years ago. It is called the Veil nebula. The delicate traceries surrounding today's midget remind me so much of that celestial sight that I named the image "Veil Nebula". After naming it, I gave it a rating of 6, since it's not at all a bad picture, though the somewhat excessively intense colors keep it from a higher rating. The image once again takes advantage of the MandelbrotBC formula, this time applied to the Z^2.003+C Mandeloid. This is the fractal with that most curious rectangular object in the Julia set of the East Valley area of the prominent midget on the infinitely-divided negative stem. I found today's scene when I went looking for that object in the JuliaBC formula, and failing to find it, turned instead to the MandelbrotBC formula to have some fun with the Mandel aspect. Using Fractint's evolver feature, I located the section with the most interesting branch cuts and started exploring. Within 10 minutes I had found a whole nest of midgets just past the midget on the stem, a stem which in this case points in the positive direction. Today's midget is a minor member of that nest. With a render time of just over 2 minutes, the parameter file is probably the best way to view the scene. But for those who enjoy travel, the file of the GIF image will soon be available on the WWW at: and at: The weather today, fractal weather that is, was near perfect. Only a slightly chilly temperature of 65F (18C) kept it from being absolutely perfect. The fractal cats helped me enjoy the day by watching me trim the grass, keeping safely out of the way whenever the mower drew near. Due to too much enjoyment, I had little time for idle philosophical pondering. I ponder best while working on dull routine jobs or while waiting for fractals to generate. I ponder very poorly while trimming lush wet grass with a lawn mower with a blade in need of sharpening. But the next FOTD is only 27 hours away, 39 hours if I don't post it until Monday morning. That is ample time in which to ponder. To see whether or not I actually ponder, check then. Until then, so long for now! Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Veil_Nebula { ; time=0:02:12.54--SF5 on a P200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 float=y center-mag=1.78204/0.00403291/4113.286/1/-99.999 params=2.003/0/1040.877965636158/0 maxiter=1500 inside=0 logmap=33 periodicity=10 colors=000J0EL0EN0HP0KR0NU0QW0TY0W_0Zb0ad0df0gf0jh\ 0mh1pk5sk8unCwnHznJzpNzpRzsWzs_zudzuhzwnzwszwuzupz\ skzphzndzkbwhYsfWndRhbPd_L_YJWYFPWCLU8HR7CP38N15L0\ 1J00H00F00C00C00A00A00A10A70AC0AJ3AP5AW8AbCAhHApJA\ wNAzRAzUNzdYznhzzuzzzzzzwzzwzzuzzuzzuzzszzswzsuwps\ wpnwpkunhunfunbsk_skYskWphUphPphNnfLnfJnfHhdAfb7db\ 3b_0__0WY0UY0RW0PW0NU0LU0PP0RL0UJ0WF0YC0_80b70d30f\ 10h00k00p00s00u00w00z00z00z00z00z00z00z00z00z00z00\ z00z00z00w00u30s73sC8pHCnNHkRNhYRfYWdYbbYf_Yk_YpdY\ hfYdhYYkYUnYNpYJsYCuY8wY3zY0zY0zY0zY0zY0zY0zY0zY0z\ Y0zY0kY0WY0FY01Y00Y00Y00Y05Y0AY0HY0WYCkNRzCfz3wz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0z } frm:MandelbrotBC { ; Formula by Andrew Coppin etal e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Guy Marson Subject: (fractint) evolver bug? Date: 29 Apr 2001 19:40:55 +0200 Hi Fractinters, in an .frm working with 4 functions (fn1-fn4) I need to play with fn1-fn3 but not with fn4. Fn4 is set to 'sinh' and has to stay so. Starting the Evolver with the 'fn4=no' option (but set to 'sinh' in the Z-screen) all the pictures are generated with 'fn4=sin' except the first one.. One more observation: I think that the first disabled function (in the evolver) is always set to sin and not to the wanted function. E.g.: fn1=random fn2=no fn3=no fn4=random then fn2 is set to 'sin' by the Evolver.. Is it a feature or a bug? cheers, Guy Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) evolver bug? Date: 29 Apr 2001 17:01:58 -0500 Guy, > Is it a feature or a bug? I'll have a look after I've finished uploading the various files for 20.1.08. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Chris Curnow" Subject: (fractint) Acknowledgments due? Date: 29 Apr 2001 23:54:55 +0100 This is a multi-part message in MIME format. ------=_NextPart_000_0019_01C0D107.CA2B8580 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable I have been interested in the various discussions regarding the = proprietary rights to fractal images. Poor old, (young), Zorba the Hutt = who spent hours generating high resolution versions of fractals to = delight others with slower machines, is then shamed into deleting them = because they are the 'property' of the esteemed Sylvie Gallet, (may her = .map files continue to delight us all). On the other hand Jim Muth, = absolutely correctly, goes to some pains to ensure that the MandelbrotBC = formula is marked as 'belonging' to Andrew Coppin et al. Surely fractal images, in the raw so to speak, are 'found' objects. = Acknowledgment is due to the creator of the formula; be it Mandelbrot = himself. The colouring scheme, however, is an aesthetic operation with = two functions. Firstly it is needed to display some features of the = 'raw image' which may not be obvious, and secondly it serves to make the = object a pleasing picture, (a piece of artwork). So we all generate or = download Jim's images every day looking for an aesthetic experience, the = maths is fun but the image is king. I have tried to better Jim's colour = scheme usually with abysmal results, so Jim you're an artist (even if = your Mum doesn't think so! 'C-FOTD 20-4-01') On the other hand I've = very often found a 'more interesting' area in one of Jim's FOTDs. (That = is, more interesting to me) - not something new that I have 'created'. As for the 'new' sinusoidal map generation utility posted by Rupert = Millard on 26th April. A note of acknowledgment that he received the = source code for the basic algorithm from me on 4th April would have been = courteous, here I *do* have a proprietary interest :-) I'm working on = using the Bezier function to define the three R, G, & B curves but the = maths is a bit steep so this utility program may be some time coming. = Any VB6 programmers interested in joining in the endeavour can contact = me direct and I'll send the source code, (and problem list!), so far. Regards, Chris Curnow curnow@mail.telepac.pt ------=_NextPart_000_0019_01C0D107.CA2B8580 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
I have been interested in=20 the various discussions regarding the proprietary rights to fractal = images.  Poor old, (young), Zorba the Hutt who spent hours = generating high=20 resolution versions of fractals to delight others with slower machines, = is then=20 shamed into deleting them because they are the 'property' of the = esteemed Sylvie=20 Gallet, (may her .map files continue to delight us all).  On the = other hand=20 Jim Muth, absolutely correctly, goes to some pains to ensure that the=20 MandelbrotBC formula is marked as 'belonging' to Andrew Coppin et=20 al.
 
Surely fractal images, in the = raw so to=20 speak, are 'found' objects.  Acknowledgment is due to the creator = of the=20 formula; be it Mandelbrot himself.  The colouring scheme, however, = is an=20 aesthetic operation with two functions.  Firstly it is needed to = display=20 some features of the 'raw image' which may not be obvious, and secondly = it=20 serves to make the object a pleasing picture, (a piece of = artwork).  So we=20 all generate or download Jim's images every day looking for an aesthetic = experience, the maths is fun but the image is king.  I have tried = to better=20 Jim's colour scheme usually with abysmal results, so Jim you're an = artist (even=20 if your Mum doesn't think so! 'C-FOTD 20-4-01')  On the other hand = I've=20 very often found a 'more interesting' area in one of Jim's FOTDs.  = (That=20 is, more interesting to me) - not something new that I have=20 'created'.
 
As for the 'new' sinusoidal = map=20 generation utility posted by Rupert Millard on 26th April.  A note = of=20 acknowledgment that he received the source code for the basic algorithm = from me=20 on 4th April would have been courteous, here I *do* have a proprietary=20 interest :-)   I'm working on using the Bezier function = to define=20 the three R, G, & B curves but the maths is a bit steep so this = utility=20 program may be some time coming.  Any VB6 programmers interested in = joining=20 in the endeavour can contact me direct and I'll send the source code, = (and=20 problem list!), so far.
 
Regards,
Chris Curnow
curnow@mail.telepac.pt<= /DIV>
 
------=_NextPart_000_0019_01C0D107.CA2B8580-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: (fractint) Fractint version 20.1.08 Date: 29 Apr 2001 18:20:26 -0500 Folks, Fractint version 20.1.08 is now available at the developer's web site. www.fractint.org Features in this patch: Added truecolor support to Fractint thanks to Bert Tyler. While in a truecolor mode, the following features are disabled/changed:\ Color Cycling\ Palette Editor brings up the contents of the MAP directory\ Saving the image still only produces a 256 color GIF\ Removed Bert's truecolor test code used with the test fractal type. Updated Paul de Leeuw's contact information. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) Acknowledgments due? Date: 30 Apr 2001 09:05:32 -0400 Hi Chris, >> Poor old, (young), Zorba the Hutt who spent hours generating high resolution versions of fractals to delight others with slower machines, i= s then shamed into deleting them because they are the 'property' of the esteemed Sylvie Gallet, (may her .map files continue to delight us all). = << Fractint and Ultra Fractal do not always generate identical images from t= he same par file. In this case, Sylvie generated the images with Fractint an= d posted Fractint pars. Zorba generated the hi-res images with UF instead = of Fractint - they appeared differently (having a different texture)than Sylvie originally generated - and so she had them removed mainly for that= reason - they were no longer her images, and so Zorba's saying that they were her images was inaccurate. Had he generated them with Fractint, she= may have approved, assuming that her permission was obtained first. I don't think Zorba was aware of the differences when he posted them. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) Fractint version 20.1.08 Date: 30 Apr 2001 09:05:33 -0400 Jonathan, >> Fractint version 20.1.08 is now available at the developer's web site.= >> Features in this patch: >> Added truecolor support to Fractint thanks to Bert Tyler. = I presume that there is no way to save a true-color par file yet either. Is there any mechanism yet for manipulating the true colors? Lee Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 30-04-01 (A Ghostly Spectre [4]) Date: 30 Apr 2001 10:01:42 -0400 (EDT) Classic FOTD -- April 30, 2001 (Rating 4) Fractal visionaries and enthusiasts: Today's hasty fractal was created by the formula 2Z^(-2.1)-2Z^(-1.9)+(1/C). I named it "A Ghostly Spectre" when I noticed that the seahorse-like detail surrounding the midget is clearly visible only when certain broad color palettes are applied to the image. With a narrow color scheme such as F2, the detail vanishes and the image becomes a featureless screen full of fractal sand. The location of today's image is in an elephant trunk in the East Valley area of a larger midget, which is resting in a chaotic part of the parent fractal. I rated the image at a 4. This is all I could give to a fractal that I found and colored with so little effort. With a running time of exactly 15 minutes, the parameter file might not be the best way of viewing the image, which will be available for download and viewing in an hour or so at: and at: One of these days when things settle down, I'm going to gain convenient access to ABPF, and resume posting the images there. But so far I haven't had the chance to recover from the move of Fractal Central auxiliary. With sunny skies and a temperature of 68F (20C), the fractal weather today was so good that I took the day off. When I returned, the cats scolded me for not being there to let them out to enjoy the fine weather. To soothe them, I gave them a treat of tuna and promised to do better next time. And speaking of next time, it will come in about 13 hours. Until then, take care, and watch out for those fractal ghosts. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Ghostly_Spectre { ; time=0:15:00.01--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.584484530091595/+1.150509782717139/7\ 774320/1/132.5 params=1/-2.1/-1/-1.9/1/300 float=y maxiter=1800 inside=0 logmap=205 periodicity=10 colors=000i_zg_zg_zfYzfYzdYzdYzbWzbWzbWzaWzaVz_Vz_\ VzYVzYTzXTzXTzSRzVTzVTzXTzXVzXVzYVzYVz_Wz_Wz_WzaWz\ aYzbYzbYzbYzd_zd_zf_zf_zf`zg`zg`zi`zibzibzkbzkbzlc\ zlczlczncznfznfzpfzphzqhzqhzqhzsizsizuizuizukzwkzw\ kzxkzxnzxnzznzzozzpzzpzzqzzqzzszztzztzztzzwzzwzzwz\ zxzzyzzzzzzzzzzzzzzxzzxzzvzzuzztzzszzpzzpzzpzzpzzn\ zxnzxnzwnxumwumwsmusmsqksqkqpjpshsqfqpdpnbplank`ni\ _lgZlfYkdXkbWiaVi_UgYTgXSfVRfSQdRPbPObONaMMaKL_JK_\ JJYHIYFHXEGXCFVAEV8DS7CS6BR4AP29P18O07O07M07M07K07\ K07J07J07H07H07F07H07F07F07F07F07E07E07E05E07C07C0\ 7C07C17C47A68A68A7BA8B8AD8CE8EE8FF7FF7HC7JE7KE7MG6\ OG6PH6RK6RL4SO4VQ4XR4YU1_V1aY1b_1b`1db0fb0gc0if0kf\ 0lh0lh0ni0pk0qk0sm0um0wn0xp0xp0zr0zr0zs0zu0zu0zw0z\ w0zx0zx0zx0zx0zx0zx0zx0zz0zz1zz1zz4zz4zz6zz6zz7zz7\ zz8zz8zzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzz\ AzzAzzAzzAzzAzzAzzAzzAzzA } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Linux Fractint Date: 30 Apr 2001 14:50:31 -0000 I don't know who did the Linux Fractint post, but HATS OFF TO THEM! Yesterday, after wanting to have a Linux Fractint for AGES, I got someone to download the source for me. I let him compile it, thinking it would be a nightmare. The guy typed "make", half a million lines of text flew past, and an executable appeared. He executed it, and it just worked. I would never have believed it if I hadn't seen it for myself! BTW, this was on an Athlon 1GHz machine. Once I reached arbitary precition mode, it was *still* rapping off 2 lines per second! Man, I *want* his machine!!! Once again, a big thanks to whoever it was who made this thing! Thanks. Andrew. _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) Acknowledgments due? Date: 30 Apr 2001 12:12:43 -0400 Hi Chris, >> Poor old, (young), Zorba the Hutt who spent hours generating high >> resolution versions of fractals to delight others with slower machines= , >> is then shamed into deleting them because they are the 'property' of t= he >> esteemed Sylvie Gallet, I can't let you say that I _shamed_ him into deleting these images. He= re is what I wrote: <<<<<<<<<<<< All of the images are different from their Fractint version, and in lot= s of them, UF replaced the nice texture with banding so, I'd like you to remove them or redo them with Fractint (maybe in a standard 1600x1200 format). >>>>>>>>>>>> Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Programmer Dude Subject: Re: (fractint) Re: C-FOTD Date: 30 Apr 2001 12:17:58 -0500 Jim Muth wrote: > When one is working with fractals, it is obvious that CPU speed is > important. I do not need to state the fact. When I do state it, I am > merely repeating the obvious. I have no memory of stating that one > should go out and spend money they cannot afford on a new computer, > though I suppose it could be implied in my words. FWIW, I've never gotten that impression from any of your FOTDs. As you say, it's self-evident that a faster machine == faster rendering, but I've never gotten the impression you were egging us on in any way. -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Chris Curnow" Subject: (fractint) No hard feelings Date: 30 Apr 2001 22:52:36 +0100 This is a multi-part message in MIME format. ------=_NextPart_000_008B_01C0D1C8.402980A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Oh dear! I really put one of Jim's cats amongst the pigeons! I owe Rupert Millard and Sylvie Gallet each a public apology. =20 Here it is Rupert. I'm sorry for implying that you 'stole' anything. =20 But it's a real bummer when you spend umpty-tump hours trying to=20 design a decent user interface for a program written only to find a=20 similar program posted! And, yes you're right; my program uses the=20 negative cos function to generate a sinusoidal curve. (And it's not=20 as good an implementation as yours!) I still think the Bezier function would transform these gradient type=20 of map generators. Really no hard feelings from my side so I'll send=20 you the bit of source to your email address, (I may persuade you to=20 spend a few moments on the 'problems'!) Sylvie, I didn't mean to imply that *you* were the one that shamed him. = (English is my native tongue but sometimes I have trouble with my = worms!) =20 The point I was trying to make was that what Zorba had done, although=20 based on your work, was something different and therefore valid; and=20 yet, he felt that he should delete them. The question still hangs = there. =20 Why did he, or anybody, feel that his version was in any way 'inferior'=20 to the original? Put it another way, how come Andy Warhole could=20 charge zillions for a picture of a can of Campbell's Soup? Was the = money=20 his, or the graphic designer who drew the original can label? =20 I suspect that Lee Skinner sums up the problem as I see it........ >Zorba generated the hi-res images with UF instead of >Fractint - they appeared differently (having a different texture)than >Sylvie originally generated - and so she had them removed mainly for = that >reason - they were no longer her images, and so Zorba's saying that = they >were her images was inaccurate. Had he generated them with Fractint, = she >may have approved, assuming that her permission was obtained first. Why ask for permission? The images were different and "no longer her = images"! Zorba gave acknowledgement that the .par files had been produced by = Sylvie=20 but he *did* feel that it was the right thing to delete them. I really = don't want=20 to put Zorba on the spot over this, so Zorba, if you're listening I'm = not asking=20 you to reply! I just don't understand; but then I'm probably being = thick! So..... any comments from the Fractint List on the premise that fractals = are=20 'found' objects, or is that a dead duck? =20 (Dead duck image copyrighted by Jan Vermeer (1623-75)=20 Still life "Dead Duck with Kalashnikov") Best regards, Chris ------=_NextPart_000_008B_01C0D1C8.402980A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Oh dear!  I really put = one of Jim's=20 cats amongst the pigeons!
I owe Rupert Millard and = Sylvie Gallet=20 each a public apology. 
 
Here it is Rupert.  I'm = sorry for=20 implying that you 'stole' anything.  
But it's a real bummer when = you spend=20 umpty-tump hours trying to
design a decent user = interface for a=20 program written only to find a
similar program posted!  = And, yes=20 you're right; my program uses the
negative cos function to = generate a=20 sinusoidal curve.  (And it's not
as good an implementation as=20 yours!)
 
I still think the Bezier = function would=20 transform these gradient type
of map generators.  = Really no hard=20 feelings from my side so I'll send
you the bit of source to your = email=20 address, (I may persuade you to
spend a few moments on the=20 'problems'!)
 
Sylvie, I didn't mean to = imply that *you*=20 were the one that shamed him. 
(English is my native tongue = but=20 sometimes I have trouble with my worms!) 
The point I was trying to = make was that=20 what Zorba had done, although
based on your work, was = something=20 different and therefore valid; and
yet, he felt that he should = delete=20 them.  The question still hangs there. 
Why did he, or anybody, feel = that his=20 version was in any way 'inferior'
to the original?  Put it = another=20 way, how come Andy Warhole could
charge zillions for a picture = of a can of=20 Campbell's Soup?  Was the money
his, or the graphic designer = who drew the=20 original can label? 
 
I suspect that Lee Skinner = sums up the=20 problem as I see it........
 
>Zorba generated the hi-res images with UF instead = of
>Fractint -=20 they appeared differently (having a different texture)than
>Sylvie = originally generated - and so she had them removed mainly for = that
>reason=20 - they were no longer her images, and so Zorba's saying that = they
>were=20 her images was inaccurate.  Had he generated them with Fractint,=20 she
>may have approved, assuming that her permission was obtained=20 first.
 
Why ask for permission?  The images were different and "no = longer her=20 images"!
Zorba gave acknowledgement that the .par files had been produced by = Sylvie=20
but he *did* feel that it was the right thing to delete them.  = I=20 really don't want
to put Zorba on the spot over this, so Zorba, if you're listening = I'm not=20 asking
you to reply!  I just don't understand; but then I'm probably=20 being thick!
 
So..... any comments from the = Fractint=20 List on the premise that fractals are
'found' objects, or is that a dead duck? 
(Dead duck image copyrighted = by Jan=20 Vermeer (1623-75)
Still life  "Dead Duck = with=20 Kalashnikov")
 
Best regards,
 
Chris
------=_NextPart_000_008B_01C0D1C8.402980A0-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Programmer Dude Subject: Re: (fractint) No hard feelings Date: 30 Apr 2001 17:18:09 -0500 Chris Curnow wrote: > Why did he, or anybody, feel that his version was in any way 'inferior' > to the original? I shouldn't speak for someone else, but perhaps not "inferior" so much as treading on private ground? Like, you can run across someone's yard, but if they indicate they don't like it, you respect that and don't? Or closer to the copyright issue: is music "discovered" or invented? You *could* suggest that--mathematically--all songs (and books) already exist as a permutation of a fairly basic set of "primatives" (notes/words). But "discovering" a permutation that pleases others, ah, that's the ART! > Put it another way, how come Andy Warhole could charge zillions for a > picture of a can of Campbell's Soup? Was the money his, or the graphic > designer who drew the original can label? (IMO obviously) His. Warhol's art was in drawing our attention to the presence of graphic art all around us in everyday life. He was pointing out that a (probably trained) artist created that soup can label. THAT's why his work is worth gazillions and mine--if I aped it--ain't. >> ...and so Zorba's saying that they were her images was inaccurate. > > Why ask for permission? The images were different and "no longer her > images"! But she did the original legwork to "discover" the image and--in a moral sense--has *some* sense of ownership which someone else might respect. > So..... any comments from the Fractint List on the premise that > fractals are 'found' objects, or is that a dead duck? Considered a dead duck by many. My vote: yeah, fractals are largely discovered, but the framing, coloring (and these days, overlaying of multiple images) is clearly art, so I don't see the answer being all Yes or all No. To me, it's the amount of effort and *personal* input by the "artist" that makes it art. If I boot FractInt, zoom in randomly for a while, generate a random color palette.... is that art? If I boot FractInt, spend a bit of time finding an image that seems pleasing to the eye, seems somewhat unique in my experience and then spend time finding a color palette that brings out the best of the fractal..... is THAT art? -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Programmer Dude Subject: Re: (fractint) Fractint version 20.1.08 Date: 30 Apr 2001 17:20:26 -0500 Jonathan Osuch wrote: > Features in this patch: > Added truecolor support... > [....] > Saving the image still only produces a 256 color GIF ??? So you can look, but not save? Given that you've GOT an image and that free PNG libraries exist, I'm curious why you can't save a t/c image? Not raggin' on ya, just curious... -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fernando Bresslau" Subject: Re: (fractint) Fractint version 20.1.08 Date: 30 Apr 2001 20:08:29 -0300 isnīt there a way of capturing the screen? maybe some third party software? Fernando Bresslau, who hasnīt tried it yet. http://www.fractal.art.br ----- Original Message ----- Sent: Monday, April 30, 2001 7:20 PM > Jonathan Osuch wrote: > > > Features in this patch: > > Added truecolor support... > > [....] > > Saving the image still only produces a 256 color GIF > > ??? So you can look, but not save? > > Given that you've GOT an image and that free PNG libraries exist, I'm > curious why you can't save a t/c image? > > Not raggin' on ya, just curious... > > -- > |_ CJSonnack _____________| How's my programming? | > |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | > |_____________________________________________|_______________________| > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Fractint version 20.1.08 Date: 30 Apr 2001 18:20:46 -0500 Chris, > ??? So you can look, but not save? Not exactly. The images you can currently generate are still using the 256 color palette. So, to save the image, the truecolor pixel on the screen is read and converted to an index value into the 256 color palette. This conversion may make the saved image look different than if it were done directly in a 256 color mode. > Given that you've GOT an image and that free PNG libraries exist, I'm > curious why you can't save a t/c image? Memory. Because of the memory model we are using (medium), we can't fit the PNG libraries into Fractint. There are solutions. We have tried compiling the Xfractint code using djgpp, but it needs work. Any volunteers? We have the experimental code which incorporates the Allegro graphics package but no way as yet to save images. We could add the PNG libraries to Xfractint and stop developing the DOS version. We will eventually have to dump the current DOS source code, but would like to at least have something place for Windows before we do this. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Fractint version 20.1.08 Date: 30 Apr 2001 18:02:36 -0500 Lee, > I presume that there is no way to save a true-color par file yet either. The images that can currently be generated still use the 256 color palette, and will generate the corresponding PAR. Once we add different coloring schemes I don't see any way to generate a PAR that makes sense. Depending on how the coloring schemes are generated. > Is there any mechanism yet for manipulating the true colors? No. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) Fractint version 20.1.08 Date: 30 Apr 2001 19:55:13 -0400 Jonathan, >> I presume that there is no way to save a true-color par file yet either.<< > The images that can currently be generated still use the 256 color palette, and will generate the corresponding PAR. Once we add different coloring schemes I don't see any way to generate a PAR that makes sense. = Depending on how the coloring schemes are generated. < I am not an Ultra Fractal user, but doesn't it generate par files of true-color images? (Perhaps some UF user could shed light on how this might be implemented.) Lee Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) C-FOTD 01-05-01 (Decorative Minibrot [6]) Date: 30 Apr 2001 23:01:26 -0400 (EDT) Classic FOTD -- May 01, 2001 (Rating 6) Fractal visionaries and enthusiasts: Before attempting to run the parameter file of today's image, notice that it has been drawn by an updated version of the MandelbrotBC formula, which I have named MandelbrotBC1. This new version is identical to the old version except that I have replaced the fixed function with a variable function, and replaced the fixed bailout radius of 100 with a variable parameter entry. Since I've lost all track of those who worked on this formula, I have credited it to 'several Fractint users'. Today's image uses the function, which curiously enough draws exactly the same images as the function. I have not yet tested the various trig functions, though hopefully they will draw some interesting if not quite correct variations. The variable bailout is useful mainly with negative-exponent fractals, which I have not yet worked with. I also see that a developer's version of Fractint with rudimentary true-color capability is available, though at the present time, one can only see the image on the screen, say 'wow', stare at the image a while, and then shut down their computer. It's a start, but before I switch the FOTD to a true- color version of Fractint, the program will need the ability to cycle and change the colors, to save the image in true-color with data intact, and also to save the true-color image as a parameter file. And there's also the possibility that my stripped-down computer, used only for finding fractals, will not be able to display true-color with its meager 1 meg of video memory. But that's a problem I'll concern myself with if and when it arises. Today's fractal is quite decorative, an attribute that inspired the name "Decorative Minibrot". The irrational number entered as the real(p1) parameter may appear familiar. Actually, it is familiar. It is the square root of 3, a number I entered hoping to create midgets with 3-way symmetry. As of yet, I have found no such midgets, though I did find today's midget, which bears a curiously close resemblance to a standard quadratic midget. Only the chopped-off main bud reveals the midget's true nature. The parameter file is unusually fast, rendering in under two minutes. Of course, the download, which may be found at: and at: is equally fast. I leave it to the viewer what route to take. The fractal weather today was clear as a crystal, with a temperature of 77F (25C), conditions that Thomas and Tippy, the fractal cats, consider ideal. Since they were deprived yester- day of their rightful time outdoors, I treated them to all the outdoor time they wanted today. My only concern is about a fox that has been seen lately in the neighborhood. The cats haven't confronted it yet, and I have no idea of what might happen if they meet. But right now, the dynamic duo are sleeping in their beds, a sign that it's time for me to shut down the fractal shoppe and call it a night. Until next time, take care, and if true-color is true, does that mean that 256-color is false? Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ DecorativeMinibrot { ; time=0:01:52.60--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=mandelbrotbc1 function=floor passes=1 center-mag=-0.73763/0.15494/2498.371/1/-124.999 params=1.732050807569/0/28.4/0 float=y maxiter=1000 inside=0 logmap=36 periodicity=10 colors=000mA9jBPnCHqDHtFDwGAzH5zH2zM4zS5zW7za8zeAz\ jMzp_zzmzzzbsfFPO0D70ID1PK4YP8cWClaGrhIwmMriPmeUha\ WcZ__VbVQfQOiMKmHGpDCuAAw45z12z00z11z42z83zC4zG4zK\ 5zO7zS8zW8y_AycByhCylClSPaAaQ0mS0pU2rU7sVCuWHvWMwY\ SyZYzZazeVmjO_pIMpMLpPKpUKpWIp_HpbHQYP2SW1WS0ZO0bL\ 0eH0hD0lB0o70s40v10y00z00z00z0ovzpszrryrpwsouumsul\ rvjpwhmwflyejzcizbfzaez_czZbzYazW_yVZwVYvUWuSVuSUs\ QSrPQpOPoOOmMMlLLlLLhKMcKOaIPYIQUHSQHUMGVKGWGFYCFZ\ AD_5Da2Cb0Cc0Be0Be0If0Pf0Wh1ch3ji4ri7sf8ueAvcCvbDw\ aFyZGzYIzWKzVLzUMzSVzKbzDiz5rz0yz0wv3vsDupOulZsiir\ furczsczscyucvucsvcpvcmwcjwchyceycbzc_zcYzcVzcUwcZ\ sccpchycfzcfzc_zeUzfMzhHyiKsjMmlO0m02o04p27r3Bs4Du\ 5Hv8KwAMyBQzCUzFYzG_zHbzIZzFWzBSz8Pz4Lz1Iz0Fz0Cz0A\ z0Dz2HzGKzUFzLAzD4z57zB8zFBzICzMFzOHzPKzPMzQPzQSzS\ VzSYzU_zUbzVezVhzWizWjzUjzQlzPlzMmzLmzImzHozGpzFpz\ DlzFWzHWzHVzIVzIVzKUzKbzY } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z| Subject: (fractint) Re: [philofractal] C-FOTD 01-05-01 (Decorative Minibrot [6]) Date: 01 May 2001 17:23:57 +1200 At 15:01 01/05/2001, Jim Muth wrote: >Classic FOTD -- May 01, 2001 (Rating 6) > >Fractal visionaries and enthusiasts: > >Today's image uses the function, which curiously enough >draws exactly the same images as the function. I have >not yet tested the various trig functions, though hopefully they >will draw some interesting if not quite correct variations. The >variable bailout is useful mainly with negative-exponent >fractals, which I have not yet worked with. Not that surprising: trunc((28.4+PI)/(2*PI)) = floor((28.4+PI)/(2*PI)). The two functions differ in how they deal with negative numbers (trunc rounds towards 0, floor rounds towards -infinity). Morgan L. Owens "I remember when all we had to worry about was good old Int." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"