From: JimMuth@aol.com Subject: (fractint) [philofractal] FOTD 29-09-01 (Aleph Null [7]) Date: 29 Sep 2001 09:42:18 EDT FOTD -- September 29, 2001 (Rating 7) Fractal visionaries and enthusiasts: Well, I didn't find a 9-rated fractal. I didn't even find one that rates an 8. But I did find a fractal that is worth a 7, and this is two points above the 5 we've been stuck with for the past several days. The iterated formula subtracts some Z^(-1.1) from Z^(1.2) before adding (1/C), and catches the parent fractal when it is on the verge of turning inside-out. With its broad textured cross and textured intricacies, today's fractal is well worth the 3 minutes required to render it from the parameter file. The name I gave it, "Aleph Null", is the name of the transfinite number that represents the least infinite of the infinity of infinities. I gave the image this name for no apparent reason. In addition to running the parameter file, the image may be seen by downloading it from the W.W.W. at: or: The fractal weather today was variably cloudy with a temperature of 64F 18C. The cats found the porch warm enough during the sunny periods, but retreated indoors when heavy clouds obscured the sun and a chilly breeze sprang up. I'll take a day or two break in my philosophical musings, but I've still got enough ideas backed up to keep me going for years. So stay tuned to the philofractal list for wisdom unlimited delivered in a moderately humble manner. That's it for today. Until next time, take care, and stay smart. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Aleph_Null { ; time=0:03:35.03--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+9.53758757820609500/+11.15144884977357\ 000/1195.65/1/47.499 params=1/1.2/-0.8/-1.1/-0.07/0 float=y maxiter=1000 inside=0 logmap=58 periodicity=20 colors=000CKoCMtDKqEJnEHkFGhGFeGDbHC`HAYI9VJ8SJ6PK\ 5MK4KMAMOFNQKPSPQUURWZTYcU_hVamXcrYewZeyLez8gvAhrB\ jnDkjElfGnbHoZJpVKkSGfPCaM9XJ5TH2WL9YOF_SLaVRcZYea\ cgeiihogdnfandZncWnaTm`Qm_NmYJmXGmVDlUAlS7lR4lQ1l`\ 5mj9nhDofHpeLpcPqaTq`XrZ`rYdsWhsUltTptRtuQxuRwpSwl\ SwhTwdTv_UvWUvSVvOVuJWuFWuBXu7Xu3Wv4Vv5Uv6Tw7Sw8Sw\ 9RxAQxBPxCOyDNyENyFSzGWzH`zHdzIizJmzJmwGmuHzsIzqJz\ oJzmKzmLzmMzmMzmPzmRwmUrmWmmYhm`cmbZmdUmgReiShlTjn\ TmpUpsVsuVuwTttStqQtoPtlOtiMsgLsdJsaIs_HsXFrUErSCr\ PBrMArKGpMMnORlQXjSaiTbjWckZdk`elcflfgmhhmkinmjnpk\ osloumpxnpzgqr`qjUqbNrWGrO9rG2r97pABnBFlCJjDNiDRgE\ VeFZcGbaHf`HcaJabL_cNYcPWdRUeTSeUZUqcZkgbekf_pjUtn\ OxrIpsPbsVet`htgkumnvsqwmtxgwybzzXzzSzzMzzHzzBzz6z\ zAzzEzzIzzLzzPzzTzzWzz_zzczzfzzjzznzzqzzhzz_zzSzzT\ zzTzzUzzUzzVzzVzzWzzWzzXzzXzzYzzYzzZzzZzz_zz_zzZzz\ ZzzYzzYzzLzzMzzSzzYzzczzi } 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================================== To unsubscribe, e-mail: philofractal-unsubscribe@lists.fractalus.com For additional commands, e-mail: philofractal-help@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 Boddington Subject: Re: (fractint) Fractal Extremes Can Predict Impending Date: 01 Oct 2001 07:48:17 -0700 At 11:47 AM 01-10-01 +1200, Morgan L Owens wrote: >How long will a steel pillar support a bridge before rust eats deep enough to >let it snap? How long will a container of corrosive acid hold before it >springs a leak? If a man makes a statement in a forest and there is no woman there to hear him...... is he still wrong? 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: kelly christiansen Subject: Re: (fractint) Fractal Extremes Can Predict Impending Breakdowns Date: 01 Oct 2001 07:53:20 -0700 (PDT) --- David Boddington wrote: > At 11:47 AM 01-10-01 +1200, Morgan L Owens wrote: > > >How long will a steel pillar support a bridge before rust eats deep enough > to > >let it snap? How long will a container of corrosive acid hold before it > >springs a leak? > > > If a man makes a statement in a forest and there is no woman there to hear > him...... > is he still wrong? > of course ===== ****************************************************************** Fractal resources available at http://cyberwizards.com/~hub/fractal To subscribe to fractaltalk, send a message to listar@wru.org with"subscribe fractaltalk" in the body. To unsubscribe from fractaltalk, send a message to listar@wru.org with"unsubscribe fractaltalk" in the body. ****************************************************************** __________________________________________________ Do You Yahoo!? Listen to your Yahoo! Mail messages from any phone. http://phone.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: "Scott D. Boyd" Subject: Re: (fractint) FOTD 29-09-01 (Aleph Null [7]) Date: 01 Oct 2001 09:59:34 -0500 Hey Jim, Oops! I don't know if anyone else received it, but I just received the FOTD from Sept. 29th. Scott 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) FOTD 29-09-01 (Aleph Null [7]) Date: 01 Oct 2001 10:05:42 -0500 Scott D. Boyd wrote: > > I don't know if anyone else received it, > but I just received the FOTD from Sept. 29th. > I just received a second copy, but it was as if it came from the Philofractal List. Maybe Damien's EZMLM mail server, or the new IP address move, is having difficulties. I know that the Development Team is definitely experiencing problems on Damien's machine. 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: Jim Muth Subject: (fractint) FOTD 01-10-01 (Spectacle [4]) Date: 01 Oct 2001 11:06:10 -0400 (EDT) FOTD -- October 01, 2001 (Rating 4) Fractal visionaries and enthusiasts: Today's fractal, which was calculated with a bailout of 400, was created by adding 0.6 parts of Z^(-16) to 6 parts of Z^(-1.6), and then adding (1/C). The parent fractal is a many-bayed affair, with more valleys than the garden here at Fractal Central has butterflies. The scene of today's image is located at the tip of a spiral filament extending from a tiny bud on the south shore of a curved valley in the north section of a secondary bay at the east end of the parent fractal. It's probably easier to zoom out of today's image and see just where it is located in relation to the whole fractal than it is to make sense of that last sentence. I named the image "Spectacle". It's true that all fractals are spectacles, (though all spectacles are not fractals). But I don't recall having used the word before, and though today's image rates only a humble 4 IMO, it is still worth being called a spectacle. The spectacular scene takes 15 minutes to unfold from the parameter file. The scene can be seen in far less time by waiting an hour or so until Paul and Scott have had a chance to post the GIF image to their web sites at: and at: and downloading it from there. (Don't ask how the image can be seen in less time than 15 minutes by waiting an hour. It's a mystery.) The fractal weather today continued chilly for the season, with clouds and a temperature of 62F 16.5C, which left the cats cold. They spent the day on their shelf by the window, watching the world outside, wishing it were warmer, and perking up only when another cat came into sight. At nightfall, a shower of rain began, but by that time, the day had already been spoiled. It's now time to shift gears into a more practical mode. When I finish the things that need to be done, I might get back to that FOTD-CD that I've been thinking of. Until next time, which will be tomorrow around this same time, take care, and be as peaceful as possible. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Spectacle { ; time=0:15:34.61--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.22164249176614300/+0.300496616260909\ 60/5.076234e+007/1/-95 params=6/-1.6/0.6/-16/0/300 float=y maxiter=3600 inside=0 logmap=243 colors=000FkzFmzKhzFmzB`z4Qz0Dw00p00i00b00Z00V40S9\ 0OF0KK0HQ0DT09Z04d00i00g00e00e00d04b07b09`0BZ0FZ0H\ X0IV0KV0OT0QS0SS0VQ0XO0ZO0`M0dK0eK0gI0iH0mH0nF0pH0\ vF0tF0rF0pF0pF0nF4mF9kDDkDHiDKgDQeDTeDXdD`b0Zk7beD\ dbKeZQiTXkQbmMgpHnrDtt9zw2zy0zz0zz0zz0zw0zv0zt0yp2\ vn4rm7ni7kg9geBebDb`FZZHVVISTKQSKSTQTVTTXZVZbX`gX`\ kZbpZdt`ewbgzbgzdizekzemzgnzdzzevzgnzigzi`zkTzmMzm\ Fzn7zp0zz0zp0zr0zk0zi2ze7udBp`FkZIfXMfTQfSTkOVpMZu\ IbzHeyFiyBmw9pvKttUwrczpmznwzkwzmwznwzpwzrrzrmzthz\ vczwczyczyczzczzUzzKzz7zz7zz9yz9yzBm0BmzzwmDwzDwzF\ wzFvzHhzHvzDzzHvzIpzMmzOgzSbzTZzXTzZQzbKzdFzgBzi4z\ k0zrTywrZzz7yzBwzFtyIrrMnmOmgSi`VgVZdQbbIdZDgXDkTF\ nSHrQItSKvSMwSOwSQySSzSTzSVzTXzTZzT`zTbzTdzTezTgzV\ izVkzVmzVnzVpzVrzVtzXvzXwzXyzXzzXzzXzzXzzTzzXzzZzz\ `zzdzzezzgzzizzmzznzzpzzrzzvzzwzzyzzzzzzzzzzzzzzzz\ zzzyzzwzzwtzzXzz9zzFzzIzz } 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: Re: (fractint) FOTD 29-09-01 (Aleph Null [7]) Date: 01 Oct 2001 11:07:30 -0400 (EDT) At 09:59 AM 10/1/01 -0500, you wrote: >Hey Jim, > >Oops! > >I don't know if anyone else received it, but I just received the FOTD from >Sept. 29th. > >Scott I got the old FOTD also. Something must have hiccoughed. 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: Michael Weitzel Subject: (fractint) Lyapunov ... Date: 01 Oct 2001 21:09:03 +0200 Hi, I have written a program for calculating the famous Lyapunov diagrams. That's the good news ;-) The bad news is that it won't run under Windows/DOS. It needs a Unix env. with X-Server (e.g. Linux; with recommended color depth of 15 bit and up). Default-formula is x(t+1)=r*x(t)*(1-x(t)) (aka "logistic"), but there 11 other (perhaps more interesting) formulas. Default sequence for parameter r is "AB" ... play with it. If you have zoomed into an area with 'weak' texture, try pressing the middle mouse button to start a recoloring function which tries to adjust the colors according to their distribution. download sources at: http://www.ldknet.org/hp/mweitzel/ljapunow_exp.tar.gz Together with this Lyapunov program comes a Mandelbrot generator which uses PVM (parallel virtual machine; to distribute the calculation over the LAN) an true color methods for incolor/outcolor. Press "j" to switch Julia-mode. I've put some examples together with some theoretic background (in german ... sorry; I will translate this page if someone is interested) on my homepage (see below). btw: maybe you will occur problems because of the "-march=i686" if your machine doesn't support it ... simply remove it. btw^2: default target for Makefile ist "ljap". If you want to try out the "Apple Man" type "make mandel". have fun :-))) -- Michael --- http://www.ldknet.org/hp/mweitzel/ *Weitzel* --- 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: "Jonathan Osuch" Subject: (fractint) Fractint version 20.2.0 Date: 01 Oct 2001 19:59:07 -0500 Folks, Fractint version 20.2.00 is now available at the developer's web site: www.fractint.org What's new: Incremented the version number to accommodate backwards compatibility for the logmap option. Modified the logmap routine so that the color with index # 2 would be displayed. Added a logmode=auto command line option that causes the logmap to adjust automatically when zooming. Changing almost anything will turn this feature off. It is best set using the screen prompt. Edited the help docs to document the move of the development area from Compuserve to the web. 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: Mark Christenson Subject: Re: (fractint) Fractint version 20.2.0 Date: 01 Oct 2001 21:46:26 -0700 At 07:59 PM 10/1/01 -0500, Jonathan wrote: >... >What's new: >... >Modified the logmap routine so that the color with index # 2 would be >displayed. Thanks for that one! I had been working around it by subtracting one from the automatic selection. >Added a logmode=auto command line option that causes the >logmap to adjust automatically when zooming. Cool! Could it also be done via the "x" menu? Or am I confusing logmode and logmap? Aloha, Bud 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) FOTD 01-10-01 (Spectacle [4]) Date: 02 Oct 2001 08:56:21 +0000 >From: Jim Muth >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >Subject: (fractint) FOTD 01-10-01 (Spectacle [4]) >Date: Mon, 1 Oct 2001 11:06:10 -0400 (EDT) > > >FOTD -- October 01, 2001 (Rating 4) Mmmm.... In my *equally* humble opinion, that should rate at least 5, but still... BTW, where I am (sunny England) it's currently 10am on the 1st of October, yet the FotD for the 1st is already up. I thought America was abotu 12 hours BEHIND GMT?... Anyone care to explane this to me? Andrew. "Where the heck IS the I.D.L. anyway???" _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp 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: "Scott D. Boyd" Subject: Re: (fractint) FOTD 01-10-01 (Spectacle [4]) Date: 02 Oct 2001 04:20:12 -0500 On Tuesday 02 October 2001 03:56, Andrew wrote: > BTW, where I am (sunny England) it's currently 10am on the 1st of October, > yet the FotD for the 1st is already up. I thought America was abotu 12 > hours BEHIND GMT?... Anyone care to explane this to me? > Starting on the east coast of the U.S., where Jim Muth is at, the EDT zone is only 4 hrs. behind GMT. There's 4 time zones for the mainland of U.S. and Hawaii is (I believe) 9 or 10 hours behind GMT. Sometimes Jim posts the FOTD to the mailing list the night before, but that doesn't happen too often. This time, Jim posted the FOTD for Oct. 1st at 11:06 EDT (or 15:06 GMT) on Oct 1st. You said it was "currently 10am on the 1st of October", but according to the email header of your email, the fractint mailing list didn't get your email until approx. 23 hours later! There's another conundrum for you! My take on it: Either Earth is spinning in reverse, (or maybe it occasionally stalls in it's orbit...) or it's just another one of those mysteries of life...... Take your pick.... Scott Boyd 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) FOTD 01-10-01 (Spectacle [4]) Date: 02 Oct 2001 11:26:04 +0000 >From: "Scott D. Boyd" >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >Subject: Re: (fractint) FOTD 01-10-01 (Spectacle [4]) >Date: Tue, 02 Oct 2001 04:20:12 -0500 > >You said it was "currently 10am on the 1st of October", but according to >the >email header of your email, the fractint mailing list didn't get your email >until approx. 23 hours later! There's another conundrum for you! > >My take on it: >Either Earth is spinning in reverse, (or maybe it occasionally stalls in >it's >orbit...) or it's just another one of those mysteries of life...... Take >your >pick.... > >Scott Boyd The trueth is far simpler... I am the proud owner of a very nice watch. But unfortunatly it's mechanical. Due to this, the poor device is under the impression that every single month of the year has 31 days in it. Thus, the watch believed that Monday was the 31 of September, and thus today is the 1st of October. So I looked at Jim's (very nice) Fractal, checked my watch and thought "kore, that's bloomin fast!" and proceeded to ask how this was possible. I have now realised that it is in fact the SECOND day of october today (aaarrrrggggh!!!!) How stupid am I? Thanks. Andrew. (PS. you don't have to answer that question!) _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp 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) FOTD 02-10-01 (Run for Cover [7]) Date: 02 Oct 2001 10:43:20 -0400 (EDT) FOTD -- October 02, 2001 (Rating 7) Fractal visionaries and enthusiasts: Today's image has been named "Run for Cover". Given the world situation, such a name would appear to have a deep psychological significance. And perhaps it does. The name came to me when I put my mind into idle. (An easy task.) It came of its own accord, like an image in an inkblot. The image's slightly sinister aura would seem to reinforce the psychological origin of the name. The formula behind the image subtracts some 1/Z from some Z, and creates a curiously distorted Mandeloid that is extremely sensitive to the value of the real(p3) parameter, being ready to expand to infinity or shrink to nothing at the slightest change of that parameter. Despite its ominous overtones, today's image rates a 7. It's also a fast image, taking only 2 minutes on a worn-out old Pentium 200mhz machine. The GIF image can also be seen by downloading it from: or from: The fractal weather today (Monday the 1st) was cloudy and cool, not the best conditions to make fractal cats happy, but the cats found what happiness they could, sleeping on the porch in the warmth of the little bit of sunlight filtering through the clouds. The temperature of 66F 19C was somewhat below average. There's so much activity on the philofractal list that I must take a day or two to digest it before offering more philosophy. And I must also keep the discussion from wandering totally away from the topic of fractals. Look for more wisdom, possibly as soon as the next FOTD. For now, I've got a day's work to finish and a couple annoying cats to feed. Until next time, take care, and a diet of fractals can really make those pounds and inches disappear. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Run_for_Cover { ; time=0:02:26.32--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.02829866980610058/-0.064453758425730\ 76/1.908413e+007/1/177.499999994679371/5.664339275\ 4018862e-009 params=-1/-1/1/1/-2.1/800 float=y maxiter=1200 inside=0 outside=summ colors=000oZctXayV_uTXrSUnRRkQOgOLdNI`MFYLCUJ9RI6N\ H3KG1NF6QEATDEWCIZBMaAQd9Vg8Zj7bm6fp5js4nu4rr5qo5q\ l5pi6pf6oc6o`6nY7nV7mS7mQ7mRJXRVHRe1Q_4QV6QQ9QLBQG\ DQBGQ6IQ1KP4MP6OP8QPASPCUPEWPGYPI_OLaONcOPeORgOTiO\ VkOXmOZnPXiQWeRUaRTYSRUTQQUNLPLHLIDHG9DD58B1BE5JI8\ QNBYSEeXHlaKofNrkQupTxtWzxZxtYvqYsmYqjYnfYlcYj_YhX\ YfTYdQYbMY`JYbMWdOVeQUgTThVSjXRk_QmaPncOpfNqhMsjLt\ mKvoJwqIvpLuoNunPtmRsmTslVrkXqjZqi`pibohdogfnfhmej\ mellaklYjkUikQhjMhjIgiEfiAei7egAafDZeGWdJTbMPaPM`R\ J_UGYXCX_9Wb6Ve3Ug0Wf1Xf2Ze3_e4ad5bd6cd7ec8fc9hbAi\ bBkaClaDmaDsdCyfBteEpeHkdKgdMbcPZcSUbVQbXLa_HabDad\ HcaLdZPeWTgTXhQ`iNdkKhlHkmFB4PHAQNGQTLQZRQcWQeVKhV\ DjU7lU1ciAWxJYsH_nGaiFcdDe_CgVBiQAkL8mG7oB6q75tCMw\ HbvIevIgvIivIkvImvIovIqZJ8YOAXTBWXCVaDUeETjFSnGRsH\ RwILhDFV9JZ9Na9Qd9Uh9Yk9`n9dr9hu9kx9luDlsHmqLmoOnm\ SnkWoiZofbpdfpbj_didbgi`e } 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: "Scott D. Boyd" Subject: Re: (fractint) FOTD 01-10-01 (Spectacle [4]) Date: 02 Oct 2001 10:34:30 -0500 On Tuesday 02 October 2001 06:26, you wrote: > From: "Scott D. Boyd" > > The trueth is far simpler... I am the proud owner of a very nice watch. But > unfortunatly it's mechanical. Due to this, the poor device is under the > impression that every single month of the year has 31 days in it. Thus, the > watch believed that Monday was the 31 of September, and thus today is the > 1st of October. > > So I looked at Jim's (very nice) Fractal, checked my watch and thought > "kore, that's bloomin fast!" and proceeded to ask how this was possible. I > have now realised that it is in fact the SECOND day of october today > (aaarrrrggggh!!!!) > Therin lies the answer to one of the mysteries of life, ie: how can an FOTD be generated before it's appointed time.... > How stupid am I? > Right - we won't go there.... Scott 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: John Lewis Subject: (fractint) OT: IDL Date: 02 Oct 2001 18:37:15 +0100 On Tue, 02 Oct 2001 08:56:21 +0000, Andrew Coppin wrote,= wondering about electronic posting dates: [cut] Andrew. "Where the heck IS the I. D. L. anyway???" Several letters before the IDS. [Obscure UK political joke] -- John Lewis, jlewis@clara.net on 10/02/2001 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: RParracho@aol.com Subject: (fractint) Formula file a couple pars Date: 02 Oct 2001 19:06:53 EDT --part1_fd.d00644f.28eba28d_boundary Content-Type: multipart/alternative; boundary="part1_fd.d00644f.28eba28d_alt_boundary" --part1_fd.d00644f.28eba28d_alt_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit i cleaned up some of my formula files and have attached it. most of them are excelent for the evolver. its to bad that no one exchanges formulas and pars any more on the list. tiltawhirl { ; 0:01:18.59 ; Created Oct 02, 2001 by Rui Parracho (c) ; Send comments to rparracho@aol.com ; Version 2001 Patchlevel 13 reset=2001 type=formula formulafile=rsp.frm formulaname=rsp_0300h4 center-mag=0/0/0.6666667 params=0.0184636982329783/-0.3060090945158239 float=y maxiter=500 bailout=256 periodicity=0 rseed=3141 colors=000000<24>nGOpHPrHQ<3>zKU<25>C46A35834<2>211000000<9>000000000<2>\ 000010030<23>0n00p00r0<3>0z0<25>0C00A0080<2>020000000<9>000000000<2>0001\ 10330<23>nn0pp0rr0<3>zz0<25>CC0AA0880<2>220000000<29>000 } fronteira { ; 0:01:02.06 ; Created Oct 02, 2001 by Rui Parracho (c) ; Send comments to rparracho@aol.com ; Version 2001 Patchlevel 13 reset=2001 type=formula formulafile=rsp.frm formulaname=Regula_falsi3 center-mag=-0.594679/0.14405/4.901961 params=-0.9143650624103519/-0.163060396130253/-0.108981597338786/0.67094\ 94308297983/0.9063692129276406/-0.7294839320047609 float=y maxiter=500 bailout=256 periodicity=0 rseed=3141 colors=CCCqz0<10>KN0GJ0DF0<3>000<10>6c07g07k0<3>Az0<10>4N03J03F0<3>000<1\ 0>0cM0gO0kQ<3>0zZ<10>0ND0JB0F9<3>000<10>8Wc9Zg9ak<3>Dmz<10>5IN4FJ4CF<3>0\ 00<10>V9cXAg_Bk<3>kFz<10>H6NF5JC4F<3>000<10>c7Xg7_k8b<3>zBo<10>N4JJ4GF3D\ <3>000<10>cMIgOKkQM<3>zYT<10>NCBJA9F87<3>000<9>bY5f`5jd6<3>zr8<8>yN4xJ3x\ F3<3>w00tz0000 } --part1_fd.d00644f.28eba28d_alt_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit i cleaned up some of my formula files and have attached it.  most of them are excelent for the evolver.  its to bad that no one exchanges formulas and pars any more on the list.  

tiltawhirl         { ;   0:01:18.59
                    ; Created Oct 02, 2001 by Rui Parracho (c)
                    ; Send comments to rparracho@aol.com
                    ;  Version 2001 Patchlevel 13
 reset=2001 type=formula formulafile=rsp.frm formulaname=rsp_0300h4
 center-mag=0/0/0.6666667
 params=0.0184636982329783/-0.3060090945158239 float=y maxiter=500
 bailout=256 periodicity=0 rseed=3141
 colors=000000<24>nGOpHPrHQ<3>zKU<25>C46A35834<2>211000000<9>000000000<2>\
 000010030<23>0n00p00r0<3>0z0<25>0C00A0080<2>020000000<9>000000000<2>0001\
 10330<23>nn0pp0rr0<3>zz0<25>CC0AA0880<2>220000000<29>000
 }

fronteira          { ;   0:01:02.06
                    ; Created Oct 02, 2001 by Rui Parracho (c)
                    ; Send comments to rparracho@aol.com
                    ;  Version 2001 Patchlevel 13
 reset=2001 type=formula formulafile=rsp.frm
 formulaname=Regula_falsi3 center-mag=-0.594679/0.14405/4.901961
 params=-0.9143650624103519/-0.163060396130253/-0.108981597338786/0.67094\
 94308297983/0.9063692129276406/-0.7294839320047609 float=y
 maxiter=500 bailout=256 periodicity=0 rseed=3141
 colors=CCCqz0<10>KN0GJ0DF0<3>000<10>6c07g07k0<3>Az0<10>4N03J03F0<3>000<1\
 0>0cM0gO0kQ<3>0zZ<10>0ND0JB0F9<3>000<10>8Wc9Zg9ak<3>Dmz<10>5IN4FJ4CF<3>0\
 00<10>V9cXAg_Bk<3>kFz<10>H6NF5JC4F<3>000<10>c7Xg7_k8b<3>zBo<10>N4JJ4GF3D\
 <3>000<10>cMIgOKkQM<3>zYT<10>NCBJA9F87<3>000<9>bY5f`5jd6<3>zr8<8>yN4xJ3x\
 F3<3>w00tz0000
 } --part1_fd.d00644f.28eba28d_alt_boundary-- --part1_fd.d00644f.28eba28d_boundary Content-Type: text/plain; name="Rsp.frm" Content-Transfer-Encoding: quoted-printable Content-Disposition: inline; filename="Rsp.frm" Testing{;Rui Parracho ;periodicity off init: z=3D0 n=3D0 loop: n=3Dn+1 z=3Dz*z+#pixel bailout: (n/|z|)<=3D 512 default: title =3D "Testing" } Scarlotta{;Rui Parracho z=3Dc=3Dpixel, : rz=3Dfn1(z)=20 z=3Dc*((rz)+sin(rz)),=20 cabs(z)<=3D 512} Scarlotta2{;Rui Parracho z=3Dpixel/pi, c=3Dpixel, : rz=3Dc/z, z=3D((rz)+sin(rz)),=20 cabs(z)<=3D 512} Scarlotta3{;Rui Parracho=20 z=3Dpixel/pi, c=3Dpixel, : rz=3Dc/z, z=3D((rz)+sin(rz)),=20 cabs(z/( (sqrt(z*z-1) + z) )) > .5} int700{;Rui Parracho z=3Dpixel, =20 if (|p1|=3D=3D0), r=3D(-3.6,1.1), else, r=3Dp1, endif : oz=3Dz, sz=3Dz-z^3/3+z^5/120, f=3Dz*z*sz, g=3D2*z*(sz)+z^2*(cos(z)), z=3Dz-r*f/g, |(z-oz)| > .0000001} Qubex{;Rui Parracho IF(|p1|=3D=3D0), a=3D(1,0), ELSE, a=3Dp1, ENDIF IF(|p2|=3D=3D0), b=3D(1,0), ELSE, b=3Dp2, ENDIF IF(|p3|=3D=3D0), c=3D(1,0), ELSE, c=3Dp3, ENDIF d=3Dpixel, ad3=3Da/3, bd2=3Db/2, ta=3D2*a z=3D(-b+sqrt(b*b-4*a*c))/ta : z2=3Dz*z, z3=3Dz2*z,=20 z=3Dad3*z3+bd2*z2+c*z+d, |z| <=3D 256} Qubexfix{;Rui Parracho IF(|p1|=3D=3D0), a=3D(3,0), ELSE, a=3Dp1, ENDIF IF(|p2|=3D=3D0), b=3D(2,0), ELSE, b=3Dp2, ENDIF IF(|p3|=3D=3D0), c=3D(1,0), ELSE, c=3Dp3, ENDIF d=3Dpixel, ad3=3Da/3, bd2=3Db/2, ta=3D2*a z=3D(-b+sqrt(b*b-4*a*c))/ta : z2=3Dz*z, z3=3Dz2*z, z=3Dad3*z3+bd2*z2+c*z+d, |z| <=3D 256} cubicQueues{;Rui Parracho IF(|p1|=3D=3D0), a=3D(3,0), ELSE, a=3Dp1, ENDIF IF(|p2|=3D=3D0), b=3D(2,0), ELSE, b=3Dp2, ENDIF IF(|p3|=3D=3D0), c=3D(1,0), ELSE, c=3Dp3, ENDIF d=3Dpixel,=20 z=3D1/3*a+1/3*c+1/3*b+1/3*sqrt(a^2-a*c-a*b+c^2-b*c+b^2) : z=3D(z-a)*(z-b)*(z-c)+d, |z| <=3D 256} Qubexnew{;Rui Parracho IF(|p1|=3D=3D0), a=3D(1,0), ELSE, a=3Dp1, ENDIF IF(|p2|=3D=3D0), b=3D(2,0), ELSE, b=3Dp2, ENDIF IF(|p3|=3D=3D0), c=3Dpixel, ELSE, c=3Dp3, ENDIF z=3D(-a+sqrt(a*a-3*b))/3 : z2=3Dz*z, z3=3Dz2*z, z=3Dz3+a*z2+b*z+c, |z| <=3D 256} Regula_falsi{;Rui Parracho IF(|p1|=3D=3D0), k=3D1, ELSE, k=3Dp1, ENDIF IF(|p2|=3D=3D0), z=3Dpixel, ELSE, z=3Dp1, ENDIF x0=3D(1,1), c=3Dx1=3Dpixel : oz=3Dz, fx0=3Dx0*x0*x0+3*x0*x0+2*x0+c, fx1=3Dx1*x1*x1+3*x1*x1+2*x1+c, z=3Dz-k*(x1-x0)*fx1/(fx1-fx0), x0=3Dx1, x1=3Dz, |z-oz| > .0000001} AutoQuad{;Rui Parracho if (cabs(p1)=3D=3D0), a=3D4, else, a=3Dp1, endif if (cabs(p2)=3D=3D0), b=3D3, else, b=3Dp2, endif if (cabs(p3)=3D=3D0), c=3D2, else, c=3Dp3, endif d=3Dpixel, z=3D(-b+sqrt(b^2-4*a*c))/a : z2=3Dz*z, z3=3Dz*z2, z4=3Dz3*z z=3D1/4*a*z4+1/3*b*z3+1/2*c*z2+d, cabs(z)<=3D256} newcube{;Rui Parracho if (cabs(p1)=3D=3D0), a=3D1, else, a=3Dp1, endif if (cabs(p2)=3D=3D0), b=3D1, else, b=3Dp2, endif if (cabs(p3)=3D=3D0), c=3Dpixel, else, c=3Dp3, endif a2=3Da*a, b2=3Db*b, c2=3Dc*c, ab=3Da*b, ac=3Da*c, bc=3Db*c,=20 m=3Da+b+c, n=3Dab+bc+ac, o=3Da*b*c,=20 det=3Dsqrt(a2+b2+c2-10*n), u=3D(det-2*m)/6, v=3D(-det-2*m)/6, if (cabs(u)>cabs(v)),z=3Du, else, z=3Dv, endif : oz=3Dz, z2=3Dz*z, z3=3Dz2*z z=3Dz3+m*z2+n*z+o cabs(z-oz) >=3D .0000001} autosquare{;Rui Parracho if (cabs(p1)=3D=3D0), a=3D1, else, a=3Dp1, endif if (cabs(p2)=3D=3D0), b=3D1, else, b=3Dp2, endif c=3Dpixel,=20 if (cabs(p3)=3D=3D0), r=3Dp1, else, r=3Dp3, endif g=3Dz=3D(-b)/(2*a) : f=3Da*z*z+b*z+c z=3Dz-r*f/g cabs(z) > .00000000128} marmelo{;Rui Parracho IF(|p1|=3D=3D0), r=3Dpixel, ELSE, r=3Dp1, ENDIF IF(|p2|=3D=3D0), x0=3D(-1,1), ELSE, x0=3Dp2, ENDIF IF(|p3|=3D=3D0), a=3Dreal(pixel), b=3Dimag(pixel),=20 ELSE, a=3Dreal(p3), b=3Dimag(p3), ENDIF z=3Dx1=3Dpixel,=20 amb=3Da-b, apb=3Da+b, tamb=3D2*amb, tapb=3D2*apb : fx0=3Dsin(amb*x0)/tamb-sin(x0*apb)/tapb+pixel, fx1=3Dsin(a*x1)*sin(b*x1), oz=3Dz z=3Dz-r*(x1-x0)*fx1/(fx1-fx0), x2=3Dz, x0=3Dx1, x1=3Dx2 |z-oz|>=3D.0000001} muitomas {;Rui Parracho IF(|p1|=3D=3D0), r=3D1, ELSE, r=3Dp1, ENDIF ;relaxation IF(|p2|=3D=3D0), a=3Dfn1(pixel), ELSE, a=3Dp2, ENDIF=20 IF(|p3|=3D=3D0), b=3Dfn2(pixel), ELSE, b=3Dp2, ENDIF=20 c=3Dfn3(pixel), z=3Dpixel, bail=3D0 p=3D9*a*c-3*b*b, q=3D2*b*b*b-9*a*b*c+27*a*a*pixel : fz0=3D a*z*z*z+b*z*z+c*z+pixel, gz0=3D 3*z*z+2*b*z+c, fz1=3D z*z*z+p*z+q, gz1=3D 3*z*z+p, u=3Dz-r*fz0/gz0, v=3Dz-r*fz1/gz1 if(cabs(u)<=3Dcabs(v)), z=3Dv, else, z=3Du, endif if((cabs(fz0)<=3D.00000001) || (cabs(fz1)<=3D.00000001)), bail=3D1, else, ba= il=3D0, endif bail<1} muitominos {;Rui Parracho IF(|p1|=3D=3D0), r=3D1, ELSE, r=3Dp1, ENDIF ;relaxation IF(|p2|=3D=3D0), a=3Dfn1(pixel), ELSE, a=3Dp2, ENDIF=20 IF(|p3|=3D=3D0), b=3Dfn2(pixel), ELSE, b=3Dp2, ENDIF=20 c=3Dfn3(pixel), z=3Dpixel, bail=3D0, p=3D9*a*c-3*b*b,=20 q=3D2*b*b*b-9*a*b*c+27*a*a : fz0=3D a*z*z*z+b*z*z+c*z+pixel, gz0=3D 3*z*z+2*b*z+c, fz1=3D z*z*z+p*z+q gz1=3D 3*z*z+p, u=3Dz-r*fz0/gz0, v=3Dz-r*fz1/gz1 if(cabs(u)<=3Dcabs(v)), z=3Du, else, z=3Dv, endif if (cabs(u-z)<=3D.00000001), bail=3D1, else, bail=3D0, endif if (cabs(v-z)<=3D.00000001), bail=3D1, else, bail=3D0, endif bail<1} outravez {;Rui Parracho IF(|p1|=3D=3D0), r=3D1, ELSE, r=3Dp1, ENDIF ;relaxation IF(|p2|=3D=3D0), a=3D3, ELSE, a=3Dp2, ENDIF=20 IF(|p3|=3D=3D0), b=3D7, ELSE, b=3Dp3, ENDIF=20 c=3Dpixel, bail=3D0,=20 z=3D(sqrt(4*b*b-12*a*c)-2*b)/6/a, : oz=3Dz, fz=3D a*z*z*z+b*z*z+c*z+pixel, gz=3D 3*z*z+b, z=3Dz-r*fz/gz if(cabs(z-oz) < .0000001), bail=3D1, else, bail=3D0, endif bail<1} ultravez {;Rui Parracho IF(|p1|=3D=3D0), r=3D1, ELSE, r=3Dp1, ENDIF ;relaxation IF(|p2|=3D=3D0), a=3Dfn1(pixel), ELSE, a=3Dp2, ENDIF=20 IF(|p3|=3D=3D0), b=3Dfn2(pixel), ELSE, b=3Dp3, ENDIF=20 c=3Dfn3(pixel), z=3D(sqrt(4*b*b-12*a*c)-2*b)/6/a, bail=3D0, p=3D9*a*c-3*b*b : z0=3Dz, fz0=3D a*z*z*z+b*z*z+c*z+pixel, gz1=3D 3*z*z+p, z=3Dz0-r*fz0/gz1 if(cabs(z-z0) < .0001), bail=3D1, else, bail=3D0, endif bail<1} volvox{;Rui Parracho z=3Dc=3Dpixel, x=3Dy=3D0, IF(|p1|=3D=3D0), d=3D1, ELSE, d=3Dp1, ENDIF : z=3Dz*z+c, x=3Dreal(z),y=3Dimag(z) cabs(2*x*x+5*y*y-8*x+10*y+3) <=3D d*cabs(x*x-7*y*y+6*x+28*y-33)} valoil{;Rui Parracho IF(|p1|=3D=3D0), z=3Dpixel, ELSE, z=3Dp1, Endif c=3Dpixel=20 : z=3Dc*((z-1/z)*log(z)-z+log(2*pi)/2) |z|<=3D 1256} maisominos {;Rui Parracho IF(|p1|=3D=3D0), r=3D1, ELSE, r=3Dp1, ENDIF ;relaxation IF(|p2|=3D=3D0), a=3Dfn1(pixel), ELSE, a=3Dp2, ENDIF=20 IF(|p3|=3D=3D0), b=3Dfn2(pixel), ELSE, b=3Dp3, ENDIF=20 c=3Dfn3(pixel), z=3Dpixel, bail=3D0 : fz0=3D z*z*z+a*z*z+b*z+c, gz0=3D 3*z*z+2*a*z+b*fn4(z) z=3Dz-r*fz0/gz0 if( (cabs(fz0)<=3D.00000001) ), bail=3D1, else, bail=3D0, endif bail<1} Beliza {;Rui Parracho IF(|p1|=3D=3D0), c=3Dpixel, ELSE, c=3Dp1, ENDIF =20 IF(|p2|=3D=3D0), z=3Dpixel, ELSE, z=3Dp2, ENDIF bail=3D0, a=3Dc*5/8, ta=3D2*a, b=3Dc*35/16, fb=3D4*b : z=3D a*sin(2*z)+b*sin(4*z), if( (cabs(z)>256) ), bail=3D1, else, bail=3D0, endif bail<1} int08{;Rui Parracho z=3Dpixel IF(|p1|=3D=3D0), r=3D1.7, ELSE, r=3Dp1, ENDIF =20 : oz=3Dz, z2=3Dz*z, z3=3Dz2*z, f=3Dlog(z3), g=3D3*z2/(z3), z=3Dz-r*f/g cabs(z-oz) > .00000001} int269{;Rui Parracho z=3Dpixel, if (cabs(p1)=3D=3D0), k=3D2.9, else, k=3D(p1), endif : oz=3Dz, f=3D.5*(sin(z))^2,=20 g=3Dsin(z)*cos(z), z=3Dz-k*f/g cabs(z-oz)> .00000001} int253{;Rui Parracho z=3Dpixel,=20 if (cabs(p1)=3D=3D0), r=3D1, else, r=3D(p1), endif : oz=3Dz f=3D.125*z-.25*sin(2*z)+.03125*sin(4*z) sz=3Dsin(z), g=3Dsz*sz*sz*sz, z=3Dz-r*f/g cabs(z-oz)> .00000001} int252{;Rui Parracho=20 z=3Dpixel,oz=3D0=20 if (cabs(p1)=3D=3D0), t=3D1, else, t=3D(p1), endif if (cabs(p2)=3D=3D0), r=3D3, else, r=3D(p2), endif if (cabs(p3)=3D=3D0), s=3D5, else, s=3D(p1), endif rms=3Dr-s, rps=3Dr+s, trms=3D2*rms, trps=3D2*rps : oz=3Dz f=3Dsin(rms*z)/trms-sin(rps*z)/trps, g=3Dsin(r*z)*sin(s*z), z=3Dz-t*f/g, cabs(z-oz) > .00000001} int304{;Rui Parracho z=3Dc=3Dpixel,=20 if (cabs(p1)=3D=3D0), k=3D1, else, k=3D(p1), endif : oz=3Dz, z2=3Dz*z, z3=3Dz2*z f=3D(3*z2-6)*cos(z)+(z3-6*z)*sin(z)+c g=3Dz3*cos(z), z=3Dz-k*f/g, cabs(z-oz) > .00000001} int303{;Rui Parracho z=3Dc=3Dpixel if (cabs(p1)=3D=3D0), k=3D1, else, k=3D(p1), endif : oz=3Dz, z2=3Dz*z f=3D2*z*cos(z)+(z2-2)*sin(z)+c, g=3Dz2*cos(z), z=3Dz-k*f/g cabs(z-oz) > .00000001} int273{;Rui Parracho z=3Dpixel if (cabs(p1)=3D=3D0), k=3D1, else, k=3D(p1), endif if (cabs(p2)=3D=3D0), m=3D.75, else, m=3D(p2), endif mp1=3Dm+1 : oz=3Dz, f=3D(sin(z))^mp1/(mp1) g=3Dcos(z)*(sin(z))^m, z=3Dz-k*f/g cabs(z-oz) > .00000001} rsp_0300w1{;Rui Parracho if (cabs(p2)=3D=3D0), c=3Dpixel, else, c=3Dp2, endif tc=3D2*c, c2=3Dc*c, tc3=3D2*c*c2, ttc=3D2*tc if (|p1|=3D=3D0), r1=3D1.5, else, r1=3Dp1, endif, if (|p2|=3D=3D0), r2=3D1.05, else, r2=3Dp2, endif, if (whitesq), r=3Dr1, else, r=3Dr2, endif z=3Dpixel, oz=3D0 : z2=3Dz*z, z3=3Dz*z2, fz=3Dz3-c2*z-tc*z2-tc3, gz=3D3*z2-c2-ttc*z, oz=3Dz, z=3Dz-r*fz/gz, cabs(oz-z) > .0000001} rsp_0300w2{;Rui Parracho if (cabs(p1)=3D=3D0), c=3Dpixel, else, c=3Dp1, endif if (cabs(p2)=3D=3D0),r1=3D(1,0), else, r1=3Dp2, endif if (cabs(p3)=3D=3D0),r2=3D(1.1,0), else, r2=3Dp3, endif tc=3D2*c, c2=3Dc*c, tc3=3D2*c*c2, ttc=3D2*tc if (whitesq), r=3Dr1, else, r=3Dr2, endif z=3Dpixel : z2=3Dz*z, z3=3Dz*z2, fz=3Dz3+c2*z+tc*z2+tc3,=20 gz=3D3*z2+c2/z+ttc*z, z=3Dz-r*fz/gz,=20 cabs(fz) > .00000001} rsp_0300w3{;Rui Parracho Julias of newton if (cabs(p1)=3D=3D0), c=3Dpixel, else, c=3Dp1, endif if (cabs(p2)=3D=3D0), r=3D(1.0,0.0), else, r=3Dp2, endif z=3Dpixel : z2=3Dz*z, z3=3Dz*z2, fz=3Dz3+z+c, gz=3D3*z2, z=3Dz-r*fz/gz, cabs(fz) > .000000001 } rsp_0400w1{;Rui Parracho if (cabs(p1)=3D=3D0), r=3D1, else, r=3Dp1, endif c=3Dpixel if (cabs(p2)=3D=3D0), a=3D(1.0,1.0), else, a=3Dp2, endif if (cabs(p3)=3D=3D0), b=3D(-1.0,-1.0), else, b=3Dp3, endif f=3Da+b+c, g=3Da*b+b*c+c*a, h=3Da*b*c z=3Dpixel;r*(c*c*c+f*c*c+g*c+h)/(3*c*c+2*f*c+g) : z2=3Dz*z, z3=3Dz*z2, fz=3Dz3+f*z2+g*z+h, gz=3D3*z2+2*f*z+g, z=3D(z-r*fz/gz)*(z-r*fz/gz)+c, cabs(fz)/.0000001 > 1 } rsp04w01{;Rui Parracho=20 c=3Dpixel if (cabs(p1)=3D=3D0), r=3D1, else, r=3Dp1, endif if (cabs(p2)=3D=3D0), z=3D(1.0,1.0), else, z=3Dp2, endif if (real(p3)=3D=3D0), m=3D(4.0,1.0), else, m=3Dreal(p2), endif m=3Dp2, mp1=3Dm+1, imp1=3D1/mp1 : f=3Dimp1*sin(z)^mp1, g=3Dcos(z)*(sin(z))^m rfg=3Dr*f/g, z2=3Dz*z, z=3Dsqr(z-rfg)+c cabs(f) > .00000001} rsp04w03{;Rui Parracho=20 ;periodicity off if (cabs(p1)=3D=3D0), r=3D1, else, r=3Dp1, endif if (cabs(p2)=3D=3D0), z=3Dpi/2, else, z=3Dp2, endif c=3Dpixel, : z2=3Dz*z, f=3Dz2*(z2*(z2+1)+1)+c, g=3D2*z*(z2*(3*z2)+1), z=3Dz-r*f/g cabs(f) > .00000001} rsp_04w5{;Rui Parracho=20 c=3Dpixel if (cabs(p2)=3D=3D0), a=3D(1.0,1.0), else, a=3Dp2, endif if (cabs(p3)=3D=3D0), b=3D(-1.0,-1.0), else, b=3Dp3, endif f=3Da+b+c, g=3Da*b+b*c+c*a, h=3Da*b*c, z=3D-c/g : z2=3Dz*z, z3=3Dz2*z, ot=3Dt t=3D3*z2+2*f*z+g, z=3D-(h+f*z2+z3)/g, |t-ot|>.000001 } rsp_04w6{;Rui Parracho c=3Dpixel if (cabs(p2)=3D=3D0), a=3D(1.0,1.0), else, a=3Dp2, endif if (cabs(p3)=3D=3D0), b=3D(-1.0,-1.0), else, b=3Dp3, endif f=3Da+b+c, g=3Da*b+b*c+c*a, h=3Da*b*c, z=3Dc/h : z2=3Dz*z, z3=3Dz2*z, z=3D-(h+f*z2+z3)/g, |z| < 256 } algria{;Rui Parracho ;makes little circlws kind of dull z=3Dc=3Dpixel : z2=3Dz*z, z3=3Dz*z*z, z=3Dz3+z2+z+c, t=3Dreal(2-(2*z+1)/(3*z2+2*z+1)) 1+t >=3D p1 } algrib{;Rui Parracho z=3Dc=3Dpixel r=3Dcabs(z) : oz=3Dz, z2=3Dz*z, z3=3Dz*z2 f=3Dz3+z2+z+c, g=3D3*z2+2*z+1, h=3D6*z+2, z=3Dz-f/(g)-p1*(g/(h)) |z-oz| > .0000001} Regula_falsi2{;Rui Parracho IF(|p1|=3D=3D0), r=3D1.65, ELSE, r=3Dp1, ENDIF IF(|p2|=3D=3D0), z=3Dpixel, ELSE, z=3Dp2, ENDIF x0=3D(1,1), x1=3Dpixel, oz=3D0 : fx0=3Dx0*x0+pixel, fx1=3Dx1*x1+pixel, oz=3Dz, z=3Dz-r*(x1-x0)*fx1/(fx1-fx0), x0=3Dx1, x1=3Dz cabs(z-oz) > .0000001} Regula_falsi3 {;Rui Parracho IF(|p1|=3D=3D0), r=3D1.65, ELSE, r=3Dp1, ENDIF IF(|p2|=3D=3D0), z=3Dpixel, ELSE, z=3Dp2, ENDIF IF(real(p3)=3D=3D0), a=3D5, ELSE, a=3Dreal(p3), ENDIF IF(imag(p3)=3D=3D0), b=3D3, ELSE, b=3Dimag(p3), ENDIF x0=3D(-1,1), x1=3Dpixel amb=3Da-b, apb=3Da+b, damb=3Damb*2, dapb=3Dapb*2 : fx0=3Dsin(amb*x)/damb-sin(x0*apb)/dapb+pixel, fx1=3Dsin(a*x1)*sin(b*x1), oz=3Dz, z=3Dz-r*(x1-x0)*fx1/(fx1-fx0), x0=3Dx1, x1=3Dz |z-oz|>.0000001} Newt_01 {;Rui Parracho z=3Dpixel, if (cabs(p1)=3D=3D0), k=3D1, else, k=3D(p1), endif if (real(p2)=3D=3D0), a=3D4, else, a=3Dreal(p2), endif if (imag(p2)=3D=3D0), b=3D3, else, b=3Dimag(p2), endif amb=3Da-b, apb=3Da+b, damb=3Damb*2, dapb=3Dapb*2 : f=3Dsin(amb*z)/damb-sin(z*apb)/dapb, g=3Dsin(a*z)*sin(b*z), oz=3Dz, z=3Dz-k*f/g, |z-oz|>=3D.0000001} Newt_02 {;Rui Parracho z=3Dpixel, if (cabs(p1)=3D=3D0), k=3D1, else, k=3D(p1), endif if (real(p2)=3D=3D0), a=3D4, else, a=3Dreal(p2), endif if (imag(p2)=3D=3D0), b=3D3, else, b=3Dimag(p2), endif amb=3Da-b, apb=3Da+b, damb=3Damb*2, dapb=3Dapb*2 : f=3Dsin(amb*z)/damb-sin(z*apb)/dapb+pixel, sinaz=3Dsin(a*z), sinbz=3Dsin(b*z) g=3Dsinaz*sinbz, h=3Db*sinaz*cos(b*z)+a*sinbz*cos(a*z) oz=3Dz, z=3Dz-k*(g/h+((g/h)^2-2*f/h)), |z-oz|>0.0000001} rsp_halley001 {;Rui Parracho z=3Dc=3Dpixel, d=3D3*pixel, z2=3Dz3=3Df=3Dg=3Dh=3Doz=3D0 if (cabs(p1)=3D=3D0), k=3D1, else, k=3D(p1), endif : z2=3Dz*z, z3=3Dz*z2+c, f=3Dz3*(c+z2) g=3Dz2*(d+5*z2), h=3D2*z*(d+10*z2) oz=3Dz, z=3Dz-k*f/(g+.5*h*(z-oz)) (|z-oz|)> 0.0000001} rsp_halley002 {;Rui Parracho z=3D10000*exp(|pixel|) c=3Dpixel, d=3D3*pixel, oz=3D0, if (cabs(p1)=3D=3D0), r=3D1.5, else, r=3D(p1), endif : z2=3Dz*z, z3=3Dz*z2, f=3Dz3*(c+z2)+c g=3Dz2*(d+5*z2), h=3D2*z*(d+10*z2) oz=3Dz, z=3Dz-r*2*f*g/(2*g*g-f*h) |oz-z|>0.000000001} rsp_ruif1{;Rui Parracho z=3D100*pixel,d=3D3*pixel c=3Dpixel,p=3D6*c, q=3D11*c*c, r=3Dp*c*c, s=3D2*p,=20 if (cabs(p1)=3D=3D0), w=3D1.5, else, w=3D(p1), endif : z2=3Dz*z, z3=3Dz*z2, f=3Dz3+p*z2+q*z+r+d g=3D3*z2+s*z+q, h=3D6*z+s, oz=3Dz z=3Dz-w*2*f*g/(2*g*g-f*h) |oz-z|>0.0000001} rsp_ruif2{;Rui Parracho z=3D0, c=3Dpixel, m=3D6*c, n=3D11*c*c, o=3Dm*c*c,=20 p=3D2*m, d=3D3*pixel, oz=3D0 if (cabs(p1)=3D=3D0), r=3D1.5, else, r=3D(p1), endif : oz=3Dz, z2=3Dz*z, z3=3Dz*z2, f=3Dz3+m*z2+n*z+o+d g=3D3*z2+p*z+n, z=3Dz-r*f/g |z-oz|>0.0000001} rsp_0300h2{;Rui Parracho z=3D100000*pixel, c=3Dpixel,p=3D6*c,=20 q=3D11*c*c, r=3Dp*c*c, s=3D2*p,=20 if (cabs(p1)=3D=3D0), r=3D1, else, r=3D(p1), endif : z2=3Dz*z, z3=3Dz*z2 f=3Dz3+p*z2+q*z+r/z g=3D3*z2+s*z+q oz=3Dz, z=3Dz-r*f/g |oz-z|>0.0000001} rsp_0300h3{;Rui Parracho z=3D10000*pixel, c=3Dpixel,p=3D6*c,=20 q=3D11*c*c, r=3Dp*c*c, s=3D2*p,=20 if (cabs(p1)=3D=3D0), r=3D(.5375,-0.7875), else, r=3D(p1), endif if (cabs(p2)=3D=3D0), s=3D(.3375,-0.10625), else, s=3D(p2), endif : z2=3Dz*z, z3=3Dz*z2 f=3Dz3+p*z2+q*z+r/z g=3D3*z2+s*z+q, h=3D6*z+s oz=3Dz, z=3Dz-r*f/g-s*g/h |z-oz|>0.0000001} rsp_regfal1{;Rui Parracho z=3Dw=3Dc=3Da=3Dpixel, n=3Dcabs(pixel) b=3Dfb=3D0, fa=3Da*a*a+a*a+a tv=3D.00000001 : z=3Dz-(a*fb-b*fa)/(fb-fa) w=3Dw*w*w+w*w+c, test=3Dreal(fa)*real(w) if(test.0000001 } rsp_0300h4{;Rui Parracho z=3Dflip(pixel), if (cabs(p1)=3D=3D0), r=3D(2.0,0.07), else, r=3D(p1), endif : fz=3Dz/(1+z*z), gz=3D(1-z*z)/(1+z*z)^2 z=3Dz-r*fz/gz cabs(gz)>.000000001 } rsp_0300h5{;Rui Parracho z=3Dc=3Dpixel if (|p1|=3D=3D0), r=3D(2.0,0.2), else, r=3Dp1, endif, : fz=3Dz/(c+z*z), gz=3D(c-z*z)/(c+z*z)^2 z=3Dz-r*fz/gz cabs(fz)>.000001} rsp_0400h1{;Rui Parracho z=3Dc=3Dpixel : x=3Dreal(z), x2=3Dx*x,x3=3Dx2*x y=3Dflip(imag(z)), y2=3Dy*y, y3=3Dy2*y z=3Dx*(x3+3*x2*y+3*x*y2+y^3)+c |z|<256} =20 rsp_04w4h1{;Rui Parracho if (cabs(p1)=3D=3D0), c=3Dpixel, else, c=3Dp1, endif z=3Dpixel : z2=3Dz*z, z3=3Dz2*z, dz=3Dz*cos(z)+sin(z)+3*z2, =20 z=3D-z3/sin(c*z), cabs(dz) > .000000001 } rsp_04w4h2{;Rui Parracho if (cabs(p1)=3D=3D0), c=3Dpixel, else, c=3Dp1, endif if (cabs(p2)=3D=3D0), z=3Dpixel, else, z=3Dp2, endif t=3D0 : z2=3Dz*z+c, z3=3Dz2*z, ot=3Dt t=3D6-4*z-20*z3, z=3Dc-1/(6-2*z-5*z3), |t-ot| > .000000001} rsp_05h01{;rui parracho =20 if (cabs(p1)=3D=3D0), p=3Dpixel, else, p=3Dp1, endif if (cabs(p2)=3D=3D0), a=3Dpixel, else, a=3Dp2, endif if (cabs(p3)=3D=3D0), b=3Dpixel, else, b=3Dp3, endif ps=3Dp*p, a2=3Da*a, b2=3Db*b, z=3Dc=3Dpixel : oz=3Dz, x=3Dreal(z), y=3Dimag(z), uz=3Dx*y*ps+(x*x-y*y-b2)*p-x*y vz=3D(x*x-a2)*ps-2*x*y*p-x*x z=3D(uz+flip(vz))-c |z-oz|>.000000064 } rsp_05h02{;rui parracho=20 c=3Dpixel if (cabs(p1)=3D=3D0), a=3Dpixel, else, a=3Dp1, endif if (cabs(p2)=3D=3D0), b=3Dpixel, else, b=3Dp2, endif k=3Da+b+c, l=3Da*b+a*c+b*c, m=3Da*b*c z=3D(sqrt(k*k-12*l)-k)/6 : oz=3Dz, z2=3Dz*z, z=3Dz*c+(k+l/z+m/z2) |z|<=3D1280 } rsp_05h03{;Rui Parracho if (cabs(p1)=3D=3D0), z=3D-.5993, else, z=3Dp1*pixel, endif if (cabs(p2)=3D=3D0), c=3Dpixel, else, c=3Dp2, endif : z2=3Dz*z, z3=3Dz2*z, z=3D-z3/sin(c*z), dz=3Dz*cos(z)+sin(z)+3*z*z, =20 cabs(dz) > .000000001 } rsp_05h04{;Rui Parracho=20 z=3Dc=3Dpixel, oz=3Dbail=3D0 if (cabs(p1)=3D=3D0), n=3D1.01, else, n=3Dp1, endif : oz=3Dz, z=3Dz*z+c if( cabs(z-oz)>.00001 ), c=3Dc*n, else, c=3Dc/n, endif if( cabs(z-oz) < .0000001 ), bail=3D1, endif if( cabs(z)>=3D64), bail=3D1, endif bail=3D=3D0 } rsp_05h05{;Rui Parracho z=3Dw=3Dv=3Dpixel if (cabs(p2)=3D=3D0), u=3Dpixel, else, u=3Dp2, endif if (cabs(p1)=3D=3D0), y=3D1.2, else, y=3D(p1), endif, k=3Du+v+w, l=3Du*v+u*w+v*w, fz=3D(sqrt(k*k-12*l)-k)/6 sz=3Dfz*fz*fz+u*fz*fz+v*fz+w tz=3Dsz*sz*sz+u*sz*sz+v*sz+w : q=3D(tz-sz)/cabs(sz-fz),=20 q2=3Dq*q, a=3Dq*tz+(q+q2)*sz+q2*fz b=3D(2*q+1)*tz+(1+2*q+q2)*sz+q2*fz c=3D(q+1)*sz, oz=3Dz, detm=3Dy*(b-sqrt(b*b-4*a*c)), detp=3Dy*(b+sqrt(b*b+4*a*c)), if(cabs(detp)>cabs(detm)), r=3Ddetm, else, r=3Ddetp, endif z=3Dz-(tz-sz)*2*c/r, fz=3Dsz, sz=3Dtz,=20 tz=3Dtz*tz*tz+u*tz*tz+v*tz+w |z-oz|> .000000001 } Autocube{;rui parracho if (cabs(p1)=3D=3D0), m=3D3*pixel, else, m=3Dp1, endif if (cabs(p2)=3D=3D0), n=3D2*pixel, else, n=3Dp1, endif p=3Dpixel, a=3Dm+n+p, b=3Dm*n+p*m+p*n, c=3Dm*n*p r1=3D(a+sqrt(m*m+n*n+p*p-b))/3 r2=3D(a-sqrt(m*m+n*n+p*p-b))/3 if (cabs(r1) < cabs(r2)), z=3Dr1, else, z=3Dr2, endif : z2=3Dz*z, z3=3Dz*z2, z=3Dz3+a*z2+b*z+c cabs(z)<=3D256 } rsp_0711h1{ if (cabs(p1)=3D=3D0), n=3D8, else, n=3D(round(cabs(p1))), endif ;points on s= tar nm1=3Dn-1, nm2=3Dn-2, a=3Dn*nm1,=20 if (cabs(p2)=3D=3D0), c=3Dpixel, else, c=3Dp2, endif ;slices with high p1 if (cabs(p3)=3D=3D0), r=3D1.5, else, r=3Dp3, endif ; looked good with 1.0 z=3Dpixel, oz=3Df=3Df1=3Df2=3D0 : oz=3Dz, f=3Dz^n-z-c, f1=3Dn*z^nm1-1, f2=3Da*z^nm2 z=3Dz-r*(2*f/f1)/(1+sqrt(1-2*f*f2/f1/f1)) CABS(z-oz)>.0000001 } Schwartian{;Rui Parracho z=3Dc=3Dpixel if (cabs(p1)=3D=3D0), r=3D1, else, r=3D(p1), endif if (cabs(p2)=3D=3D0), k=3D1, else, k=3D(p2), endif if (cabs(p3)=3D=3D0), test=3D4, else, test=3D(p3), endif : f=3Dz*z*z+fn1(z),=20 g=3D3*z*z+fn2(z), h=3D6*z+c z=3Dz-r*(k/g-3*h*h/2/g/g)/f cabs(z)< test } Weier{;Rui Parracho if (cabs(p1)=3D=3D0), k=3D1, else, k=3D(p1), endif z=3Dc=3Dpixel : z=3Dz*z+c Sin(z*flip(1))/(Exp(2*z+1))<=3Dk } Weiers{;Rui Parracho z=3Dc=3Dpixel : fz=3Dfn1(2*z), z=3D1-fn1(z*z+c) cabs(fz/(1+z)) > cabs(fz)/c } Cubix{;Rui Parracho d=3Dpixel if (cabs(p1)=3D=3D0), a=3D(1,2), else, a=3Dp1, endif if (cabs(p2)=3D=3D0), b=3D(3,1), else, b=3Dp2, endif if (cabs(p3)=3D=3D0), c=3D(1,-1), else, c=3Dp3, endif zp=3D(sqrt(b*b-3*a*c)-b)/3/a ;zn=3D(sqrt(-b*b-3*a*c)-b)/3/a ;if (cabs(zp) < cabs(zn)), z=3Dzn, else, z=3Dzp, endif z=3Dzp : z2=3Dz*z, z3=3Dz*z2 z=3Da*z3+b*z2+c*z+d cabs(z)<=3D256 } Cubix1{;Rui Parracho if (cabs(p1)=3D=3D0), a=3D(1,2), else, a=3Dp1, endif if (cabs(p2)=3D=3D0), b=3D(3,1), else, b=3Dp2, endif c=3Dpixel sumc=3Da+b+c, sumcs=3Da*a+b*b+c*c, sump=3Da*b+a*c+b*c zp=3D(-sumc+sqrt(sumcs-sump))/3 zn=3D(-sumc-sqrt(sumcs-sump))/3 If (cabs(zp) < cabs(zn)), z=3Dzp, else, z=3Dzn, endif : z=3D(z+a)*(z+b)*(z+c) cabs(z)<=3D256 } --part1_fd.d00644f.28eba28d_boundary-- 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 20.2.0 Date: 02 Oct 2001 18:31:33 -0500 Bud, >>Added a logmode=auto command line option that causes the >>logmap to adjust automatically when zooming. >Cool! Could it also be done via the "x" menu? Or am I confusing >logmode and logmap? Logmode and logmap are related. I would have liked to been able to add this feature to the logmap selections on the "x" menu, but that would have involved changing the data type for the logmap screen prompt. I'm not inclined to do that at this point. 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: bmc1@airmail.net Subject: Re: (fractint) FOTD 02-10-01 (Run for Cover [7]) Date: 03 Oct 2001 01:38:50 -0500 Fractaliers -

Sorry for the OT, but I can't deal w/ Philofractal Disc Grp in its entirety yet.

Just wondering whether anyone else out there has had a look yet at (and comment re) Wolframs' latest 12-lb, 992-pg, "baby" called "A New Kind of Science" ?

I quote briefly from the self-promotional blurb on amazon.com's site:

    This long-awaited work from one of the world's most respected scientists presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe.
    Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
    Written with exceptional clarity, and illustrated by more than a thousand original pictures, this seminal book allows scientists and non-scientists alike to participate in what promises to be a major intellectual revolution.

Is this just a touch over the top?????
 

D. Freed
 

Jim Muth wrote:

FOTD -- October 02, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Today's image has been named "Run for Cover".  Given the world
situation, such a name would appear to have a deep psychological
significance.  And perhaps it does.  The name came to me when I
put my mind into idle.  (An easy task.)  It came of its own
accord, like an image in an inkblot.  The image's slightly
sinister aura would seem to reinforce the psychological origin
of the name.

The formula behind the image subtracts some 1/Z from some Z, and
creates a curiously distorted Mandeloid that is extremely
sensitive to the value of the real(p3) parameter, being ready to
expand to infinity or shrink to nothing at the slightest change
of that parameter.

Despite its ominous overtones, today's image rates a 7.  It's
also a fast image, taking only 2 minutes on a worn-out old
Pentium 200mhz machine.  The GIF image can also be seen by
downloading it from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today (Monday the 1st) was cloudy and cool,
not the best conditions to make fractal cats happy, but the cats
found what happiness they could, sleeping on the porch in the
warmth of the little bit of sunlight filtering through the
clouds.  The temperature of 66F 19C was somewhat below average.

There's so much activity on the philofractal list that I must
take a day or two to digest it before offering more philosophy.
And I must also keep the discussion from wandering totally away
from the topic of fractals.  Look for more wisdom, possibly as
soon as the next FOTD.

For now, I've got a day's work to finish and a couple annoying
cats to feed.  Until next time, take care, and a diet of
fractals can really make those pounds and inches disappear.

Jim Muth
jamth@mindspring.com

START 20.0 PAR-FORMULA FILE================================

Run_for_Cover      { ; time=0:02:26.32--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.02829866980610058/-0.064453758425730\
  76/1.908413e+007/1/177.499999994679371/5.664339275\
  4018862e-009 params=-1/-1/1/1/-2.1/800 float=y
  maxiter=1200 inside=0 outside=summ
  colors=000oZctXayV_uTXrSUnRRkQOgOLdNI`MFYLCUJ9RI6N\
  H3KG1NF6QEATDEWCIZBMaAQd9Vg8Zj7bm6fp5js4nu4rr5qo5q\
  l5pi6pf6oc6o`6nY7nV7mS7mQ7mRJXRVHRe1Q_4QV6QQ9QLBQG\
  DQBGQ6IQ1KP4MP6OP8QPASPCUPEWPGYPI_OLaONcOPeORgOTiO\
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  mellaklYjkUikQhjMhjIgiEfiAei7egAafDZeGWdJTbMPaPM`R\
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  bBkaClaDmaDsdCyfBteEpeHkdKgdMbcPZcSUbVQbXLa_HabDad\
  HcaLdZPeWTgTXhQ`iNdkKhlHkmFB4PHAQNGQTLQZRQcWQeVKhV\
  DjU7lU1ciAWxJYsH_nGaiFcdDe_CgVBiQAkL8mG7oB6q75tCMw\
  HbvIevIgvIivIkvImvIovIqZJ8YOAXTBWXCVaDUeETjFSnGRsH\
  RwILhDFV9JZ9Na9Qd9Uh9Yk9`n9dr9hu9kx9luDlsHmqLmoOnm\
  SnkWoiZofbpdfpbj_didbgi`e
  }

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==================================

--------------------------------------------------------------
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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: kelly christiansen Subject: Re: (fractint) FOTD 02-10-01 (Run for Cover [7]) Date: 03 Oct 2001 06:04:36 -0700 (PDT)

Is this just a touch over the top????? sounds like standard marketing Hype to me. ===== ****************************************************************** Fractal resources available at http://cyberwizards.com/~hub/fractal To subscribe to fractaltalk, send a message to listar@wru.org with"subscribe fractaltalk" in the body. To unsubscribe from fractaltalk, send a message to listar@wru.org with"unsubscribe fractaltalk" in the body. ****************************************************************** __________________________________________________ Do You Yahoo!? Listen to your Yahoo! Mail messages from any phone. http://phone.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) FOTD 03-10-01 (Pi in the Sky [5]) Date: 03 Oct 2001 10:56:22 EDT FOTD -- October 03, 2001 (Rating 5) Fractal visionaries and enthusiasts: There is a 'zexpe' fractal -- the fractal formed by the formula Z^2.7182...+C, and named by Lee Skinner. Now we have a 'zexpi' fractal, which naturally is formed by the formula Z^3.1416...+C. Like all fractals created from fractional powers of Z, the zexpi fractal is infinite in surface extent as well as depth. The MandelbrotBC1 Fractint formula can explore the more remote parts of the infinite surface extent of these fractional fractals. Setting the real(p2) parameter to the number pi, causes the formula to draw 'ground level', but who wants to sit at ground level when there are limitless heights to scale? For today's fractal I went up 189 floors from ground level, until I found a level where the zexpi fractal really does things. The midget at the center of today's image lies in the suburbs of a larger midget, which lies in the suburbs of a still larger midget, and so on about 6 times, until we reach a midget that lies in an area of chaos on the northwest shore of the main bay of the parent fractal, which is the one mentioned above, that really does things. I named the image "Pi in the Sky" not in mockery of religious beliefs, but rather because it is an accurate description of the image and its location in relation to the entire infinite fractal. The rating of the image is not quite as high as its location, but with a rating of 5 the image is worth the effort of running the parameter file, or the lesser effort of downloading the image from: or from: The fractal weather today featured a big warm-up, with brilliant sunshine and a temperature of 77F 25C. The fractal cats took up residence on the porch before lunch time, and stayed there until near sunset. That's it for now, fractal fans. Until next time, take care, and we don't even know what we don't know. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Pi_in_the_Sky { ; time=0:17:28.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.89071956777594660/+0.395577680067524\ 30/1.086197e+012/1/45.000916072899642/-0.007023192\ 99345871562 params=3.14159265358979/0/189/0 float=y maxiter=3600 inside=0 logmap=518 colors=000jCZlFXmHUoKSqNQrPNtSLvVJwXGy_EzaCw_BuYBs\ WBqUAoSAmQAjO9hM9fK9dI8bG8`E8ZD8XG7VI7TK7RM7PO7NQ7\ LS7JU7HW7FY7D_7Ba79c77e75g74i75kD6lI7mO8nT9oZApcBq\ iBrnEkhGdcIZZKSTMLOOFJPJMQMOQPQRSTRVVSYXS`ZTdaTgcU\ jeUmgVpjVslWvnWypVxoUwoUwnTvnSumSumRtlQslQskPrkOqj\ OqjNpiOoiQoiSglU`nWTqYMs_Eva7xc0ze1yg1xi1wk1wl1vm1\ un1to1tp1sq1rr1qs1qt2su3tv4uw5vx6wy7xz8yg2Mh7LhBKh\ GKhKJiPIiTIiYHiaHfbIdbIbcI`cIYcIWdIUdISdITaMTZQTWU\ TTYUQaUNeUKiUHmTGnSGoRGpQGqPGrOGsNGtMGuLGvKGwKGxJF\ wJFwIEwIEwIEvHDvHDvHDvGBpG9jG7dG5ZG3UI5VK6VL8WN9WO\ AWQCXRDXTEXVGYWHYYIYZKZ`LZaMZdLbfKehJhjIklHnoKeqNY\ tQPvSHPhZVk_`n_fq_lt`rw`xy`wtZwpYvkXvgVubUuWTtSRtR\ QsSPsTNrUMrVLqWMpXNoYOnZPn_Qm`RlaSkbTkcUjeVigWhiXh\ kYom_vo`wqPysDzu1ww2ux2ry2pz3mz3kz3iz4fz4dz4az5_z5\ Yz5Zz9_zD`zHazLbzPczTdzXez`fzdgzhgzkeziczhbzf`ze_z\ cYzbXz`Vz_TzZSzXSzL`zUhza } 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: FOTD 03-10-01 (Pi in the Sky [5]) Date: 03 Oct 2001 12:25:39 -0500 JimMuth@aol.com wrote today: > > FOTD -- October 03, 2001 (Rating 5) > ....MandelbrotBC1 Fractint formula.... > I named the image "Pi in the Sky".... > > START 20.0 PAR-FORMULA FILE================================ > > Pi_in_the_Sky { ; time=0:17:28.25--SF5 on a P200 > reset=2002 type=formula formulafile=allinone.frm > formulaname=MandelbrotBC1 function=floor passes=1 > JimMuth@aol.com wrote a few months ago: > > Classic FOTD -- April 19, 2001 (Rating 6) > ....rendered by Andrew's MandelbrotBC formula. > ....and named it "Pi in the Sky". > > 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 > You may wish to name today's PAR with at least a #2. :-) 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) FOTD 04-10-01 (Tinseled Minibrot [6]) Date: 04 Oct 2001 11:11:44 EDT FOTD -- October 04, 2001 (Rating 6) Fractal visionaries and enthusiasts: Just a quick comment today, since I'm late and there's a lot of work to be done. The iterated formula adds some Z^(1.1) to some Z^(-0.9) and then adds 1/C. The result is a grossly distorted Mandeloid, with a large two-lobed bay and a main bud so shrunken as to be virtually invisible. Today's image lies on the north shore of the main bay. I named the picture "Tinseled Minibrot". I had to give it *some* name and time was short. The rating of 6 was also hastily arrived at, but it seems fairly accurate. With a render time of 23 minutes, the parameter file borders on being annoyingly slow. The download is far more efficient. That download may be found at: and at: The fractal weather today was mid-summer like, with hot sun and a temperature of 84F 29C. The fractal cats approved by sleeping peacefully. I've no time for philosophy today, but I have much material backed up and ready to break loose on the philofractal list. Tomorrow could be the day. And now it's off to work. Until next time, take care, and keep the fractals coming. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Tinseled_Minibrot { ; time=0:23:44.28--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-5.02405328436573600/+7.107839233804552\ 00/4.135209e+008/1/147.499710220384458/0.000806182\ 515984486814 params=1/-0.9/1/1.1/-0.15/0 float=y maxiter=2400 inside=0 logmap=465 periodicity=25 colors=000O6PN8QN9RNBSNCTPIOQOKRUFT_BUe6Vj2LnJBq_1\ to8mnFgmL`lSVkZOjdIikBhq5gk7ef9d`BbWCaQE`LGZFIYAJX\ CP`EVdF`hHflJlpKqtVnkelcpjWm_QkQKiGEg69XFMNNZDVk3b\ xCU_LLCHHIEEOABT77Z34d01i84iF6iM8iTAi`DigFinHiuJiV\ BS43A41B40CWOavjztess`lrWeqSZpNSoILnDEm97nONoabooq\ igoc`mYTkSMiNFgc81gHBjPLnXUqdculmxtvsmpnfji_deTZ`M\ TWFNS8I_8Ig8Io8Iw8IvCKvGLvKMvONvSOvWPmZZdahXcq3FqB\ PjJYcQfXYZ`eRdmKgkPeiUcgZaeb`ZXaTSaMMaGHa9Ba36aD5U\ M5NW5Gd59f9OhCbjFqZNpOVpDbp2jpAenHalPXjWThcOfjKe8h\ aA``CU_ENZGGYI9XK2X5YaENbMDcU3cSEZRPVQ_RPjNOuJPkOQ\ aTQSXRXYRaZRf_Sk`SpaStaPsdMrgJqjGpmEpoHs6SS6a16X2F\ T2NO3VK3bO7dSAeWDg_GhcKigNkkQlnTmfWiZZeR`bVQYYFT`4\ PgB_mIjsPujYpbekVmfNubRqaUm`Xi__eZbcZ`ca_cdYcgXcjW\ clXciYcfZcc_c`feI`hHWkGQnFLqEFtDAwC5zCNzEPzKUzQZzW\ czahzgmzmrzswzlzzfzz`zzVzzOzzIzzCzz6zzgzzhzzHzzFzz\ GzzHzzIzzJzzKzzLzzLzzNzzO } 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) FOTD 05-10-01 (The Goofiest Fractal [6]) Date: 05 Oct 2001 11:10:31 EDT FOTD -- October 05, 2001 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is filled with those goofy looking, cross-eyed, double spirals that characterize the East valley areas of midgets. The eyes are everywhere. There are so many of them that I had no choice but to name today's image "The Goofiest Fractal". Well, I guess I did have a choice, but I decided on the name because I like it. The iterated formula subtracts Z^20 from Z^7 and adds C. The resulting fractal is an unassuming affair with X-axis symmetry and a curious dimple on the eastern border of the main bay. Within this dimple lies a fragment of an east valley. Unlike the East Valley of the classic Mandelbrot set, this valley has a row of midgets along its center line. These midgets are surrounded by the typical goofy-eyed Julia features of East Valley. Today's midget lies buried deep in one of the goofy- eyed spirals in the pattern around one of these larger midgets. This explains why today's image swarms with double spirals. I rated the picture at a slightly above average 6. At one time I briefly considered a rating of 7, but a second look convinced me that a rating of 6 would be the most honest. With its render time of 14 minutes or less, the parameter file is a bit on the slow side. With a download time of one minute or less, downloading the GIF files from the W.W.W. is the more efficient way to see the image. The GIF image files will be available in a few minutes on the W.W.Web at: and at: A perfect sunny midsummer-like day in early Autumn today here at Fractal Central made the cats happy. The temperature, which should be around 70F 21C, actually reached 84F 29C. The cats showed their happiness by sleeping most of the afternoon. I'm considering the direction the FOTD is taking. Perhaps it's time to leave the world of Minibrots for a while, and get back to that four-dimensional (five-dimensional when time is included) stuff I was doing a while back with the Julibrot figure. We'll see how I feel in the days to come. I'll be more relaxed when I get the day's work finished, and the way to get finished is to get started. So until tomorrow, take care, and finish what you're doing, so you can enjoy the fractals without distraction. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ TheGoofiestFractal { ; time=0:14:06.51--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.62576838904586850/+0.000016702092589\ 72/8.099607e+009 params=1/7/-1/20/0/0 float=y maxiter=1500 inside=0 logmap=-274 periodicity=0 colors=000_UISOELI9ED5IF6LG6OH6RI6UJ7XK7_L7bM7ZLCV\ LGRLKNKPJKTFKXBK`9Oc7Rf5Ui3Xl2_n4Vh6Qc8LZAGUCBPD7K\ MIJUOIaWHicGqkFpkEokDnkCmlBllAklAilAhmAgmAfmCenFdn\ IgnLlnOqnQsiTtdVv_XwVZyQ`zLbwEXr8RmAPhCNcELZGKUKIP\ LGKNEGQDETHCXLA`O8dN7hM6lLApKKrUUmcccjhUfiObfSZbXU\ _`QXdMUhISdMR`QPYUOUXMR`LNdKKgGIcDH`AFX7EU4DRGEISF\ AbG2aK4aN5`Q6`T7`W8_Z9_aA_dBU`FPXJKTNFPRALV5HZ0Ea4\ K_7QZBWXEZWHaULdTPeRTcQXZk`UldPmeKnhMokPolTlmWim_g\ nbdocaoc_pcXpcVhcWacWUdWNaWGZWJVVLSVNOVQLVSHVUEVQF\ XNGZKH_HIaEJbLQZRWWXaSbgPhmMjfJk_HlTFkONhPQcPTZPWU\ PZPQaKRdJUgKXjKVgLSeLQbMS`MUYNWWOYTO_RPaOPcMQeJQgH\ OiLMkPKmSIoWGq_EtbCwfBziGzhKzhPzgTzgXzfazfezeizeez\ WbzMZzCWz3Xz7XzAXzDXzGXzJXzMXzPXzSXzVXzYXz`XzcXzfX\ ziQzfJzcCz`6zZ5zX4zW3zU2zT2zS9zTFzULzVRzWXzXbzYhzZ\ nz_tz`zz`izOTzCCz0HzCLzOPz_TzkSzlRzlRzmQzmQznPznPz\ oOzoNzpNzpMzqMzqLzrmzRfzN } 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) FOTD 06-10-01 (Mandelbrot Midget [5]) Date: 06 Oct 2001 11:04:22 EDT FOTD -- October 06, 2001 (Rating 5) Fractal visionaries and enthusiasts: Today's FOTD pictures a midget located in the Scepter Valley area of the Mandelbrot set. This midget has existed for all eternity, unseen and unknown, waiting patiently for some intrepid fractalist to stumble upon it and present it for the whole world to see and admire. I am that fractalist. The midget's time to shine will be brief. Within 24 hours the next FOTD will appear. This next FOTD may rate higher than today's image, and today's will then be forgotten. It will return to the shadows of unseen things to lurk there for all eternity. But all is not lost for the little midget. There are theories that an infinity of parallel universes exist, and if this is so, the midget has already been revealed an infinity of times. In fact every midget that exists in the infinite depths of the infinity of fractals has been revealed an infinity of times. I named today's image "Mandelbrot Midget" because that's what it is. And now, in my infinite wisdom and deep humility, I will humbly recommend that everyone take at least a brief glance at the perfectly average 5-rated midget, here making its debut. The parameter file runs in only 39 seconds. Those who would rather not hassle themselves with parameter files can download the image from the W.W.Web at: and at: The fractal weather today was once again summer-like, though not quite as warm as yesterday. The warm sun and temperature of 80F 26.5C made conditions perfect for both man and cats. The man had to work most of the day; the cats slept most of the day, though they found the energy to rush to the window, bristling, hissing and growling when a prowling tomcat wandered a bit too close. It's now time to start my well-earned week-end. Maybe, if I try hard enough, I'll manage to get through the entire week-end without doing any serious work. (Finding fractals is not serious work.) Until 24 hours from now, when the next FOTD will appear, take care, and be fractally oriented. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Midget { ; time=0:00:39.49--SF5 on a P200 reset=2002 type=mandel center-mag=-1.2539829697176\ 28/+0.02311723341662286/1.072149e+010/1/175.000011\ 138620039/-6.90021355569114814e-005 params=0/0 float=y maxiter=5000 inside=0 logmap=812 colors=000VFdVFfVHgVHiVIkUIlUKnUKqUMrUMtUNuSNwSPyS\ PzSRzSRzSSzRSzRUzRUzRVzRVzRXzSYzRWzPVzPUzNSzMRzMPz\ KMwIKtIIqHHnFFkFDgDCdC8cC6`A4X83U81R60N40K40H30D10\ A106003000000000100300600A00C00F00H00K00N00P00S00U\ 00X00`00a00d00f00i00l00n00q00r00u00y00z00z00z00z00\ z00z01z03z04z06z08z0Az1Cz3Dz4Fz6Hz8IzAKzCMzDNzFPzI\ RzKSzMUzNVzPXzRYzS`zUazVczYdz`fzagzcizdkzflzgnzioz\ kqznrzotzquzrwztyzuzzwzzyzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzyyywyyuwwtwuruurutqtrotrnrqlrokqoiqniqlgolfokdn\ icnialg`lf`kfYkdXicVicUgaSg`Rf`RfYPdXNdXMcVKcUIaUH\ aSH`RF`RDYPCYNAXN8XM6UJHPGKKC6F30H40H60I80IA0IA0KC\ 0KD0MF0MH0MH0NI0NK0NM0PM0PN0RP0RR0RS0SS0SU0SV0UX0U\ Y0VY0V`1Va1Xc1Xc3Yd3Yf3Yg4`i4`i4`k6al6an6co8co8cq8\ drAdtAfu8dtAdtAdtAdtAdtActCctCcuCcuCcuCawDawDawDay\ DayD`zD`zH`zH`zH`zH`zH`zH } 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: "Les St Clair" Subject: Re: (fractint) Formula file a couple pars Date: 06 Oct 2001 19:57:23 +0100 Hi Rui > most of them are excelent for the evolver. its to bad that no one exchanges formulas and pars any more on the list.< Yes, evolver is a great feature. Here's a couple back at ya... cheers, Les evolved_01 { ; evolved from Rui Parracho's "tiltawhirl" t= 0:02:47.58 ; t=calc time [h:mm:ss.] using PIII 600 at 1600x1200 ; (c) 2001 by Les St Clair ; http://www.les.stclair.btinternet.co.uk/ ; parameters created on Oct 06, 2001 ; Version 2001 Patchlevel 13 reset=2001 type=formula formulafile=rsp.frm formulaname=rsp_0300h4 passes=t center-mag=-0.771795/-0.895232/0.8487505 params=-2.08905301065096/0.5710013122959074 float=y maxiter=500 bailout=256 outside=atan periodicity=0 rseed=3141 sound=off colors=0004lb<2>3`U3XR3VP<3>2JG1GE1DC<3>1OK1QN1TP<2>1aV2dY2ha<3>4zp<25>2\ KH2IG2GE2FD2DC2BA<10>133133122111<12>000000000<3>000500500<20>_82a82b92<\ 3>iB3<3>oPAqSCsWE<2>xeKziMyfL<3>rTDpPBoM9<2>iB3<5>O52K42H31<3>000<9>000<\ 3>000011021<7>286297298<2>3CA3CA3B9<10>143133132<3>000<3>2862A83CA<6>9_R\ AbTBfW<3>Fte<9>6MH5JF4FC<2>155012000<9>2bV2fZ3ja<3>4zn<2>4pe } evolved_02 { ; evolved from Rui Parracho's "tiltawhirl" t= 0:02:31.10 ; t=calc time [h:mm:ss.] using PIII 600 at 1600x1200 ; (c) 2001 by Les St Clair ; http://www.les.stclair.btinternet.co.uk/ ; parameters created on Oct 06, 2001 ; Version 2001 Patchlevel 13 reset=2001 type=formula formulafile=rsp.frm formulaname=rsp_0300h4 passes=t center-mag=0.658369/0.903322/3.267681/1/90 params=-0.1181371501815853/-1.031861323892941 float=y maxiter=500 bailout=256 outside=atan periodicity=0 rseed=3141 sound=off colors=000GQV<3>ORTQRTSRS<3>_UOaUNcVM<2>iWJkXIkYK<8>pkeqlgqnj<2>srqttttt\ t<103>555555444<2>333222444<7>KKKMMMOOO<3>XXX<11>JJJIIIHHHFFFEEE<5>DDDDD\ DEEE<18>HHHHHHHHHHHHHHHIII<2>EEE<4>OOOQQQSSS<3>bbbeeehhh<12>RRRQQQOOO<3>\ III<3>QQQ<8>HQU } evolved_03 { ; evolved from Rui Parracho's "tiltawhirl" t= 0:07:10.46 ; t=calc time [h:mm:ss.] using PIII 600 at 1600x1200 ; (c) 2001 by Les St Clair ; http://www.les.stclair.btinternet.co.uk/ ; parameters created on Oct 06, 2001 ; Version 2001 Patchlevel 13 reset=2001 type=formula formulafile=rsp.frm formulaname=rsp_0300h4 passes=t center-mag=0.242758/0.844807/1.394285/1/30 params=-1.616077150791955/-0.9059724723044527 float=y maxiter=500 bailout=256 outside=atan periodicity=0 rseed=3141 sound=off colors=xn_los<3>XZ`SUXOQS<3>788<3>222000001<6>11911A21B<10>35O36P36Q37R<\ 3>59Y6AZ6B`7Bb7Cd<26>PWtQXtQXu<2>T_wT_wSZv<25>CHgBGfAGe<2>8Dc7Cb7B`<7>35\ O24M24K13J12H01F<10>017016016<2>003001001<7>STWVX_Z`c<3>los<8>ZXSYVPWTL<\ 2>SNCQL9QL9QL8QK7<21>pgTqhUsiV<2>vlYxn_xn_xn_<24>XQCVPBUOA<2>RL7QK6QK7QL\ 9<2>UQHVSKXUO<8>jlo } evolved_04 { ; evolved from Rui Parracho's "tiltawhirl" t= 0:01:27.93 ; t=calc time [h:mm:ss.] using PIII 600 at 1600x1200 ; (c) 2001 by Les St Clair ; http://www.les.stclair.btinternet.co.uk/ ; parameters created on Oct 06, 2001 ; Version 2001 Patchlevel 13 reset=2001 type=formula formulafile=rsp.frm formulaname=rsp_0300h4 passes=t center-mag=0.00714271/-0.0268822/0.5481566/1/12.5 params=-1.279702139347514/1.652272103030488 float=y maxiter=500 bailout=256 outside=atan periodicity=0 rseed=3141 sound=off colors=000q04<4>e1Ab1B`1C<3>R1HO2JN2I<7>B19A18817<3>212000000<23>J1EK1FL\ 1F<2>N1HO2IN2K<8>A1i81l71n<2>21w00z03z<8>0bz0fz0jz<3>0zz<25>0Cz0Az08z<2>\ 02z00z00y<11>91hA1gB1e<2>D1aD1`C1Z<15>319317215214112000<18>L1CM1DN1E<2>\ Q1GS2HV2G<5>h19k18m17<3>w12z00z20<17>zk0zm0zp0<3>zz0<16>zH0zE0zB0<2>z30z\ 00x01v02s03 } frm:rsp_0300h4{;Rui Parracho z=flip(pixel), if (cabs(p1)==0), r=(2.0,0.07), else, r=(p1), endif : fz=z/(1+z*z), gz=(1-z*z)/(1+z*z)^2 z=z-r*fz/gz cabs(gz)>.000000001 } 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: John Lewis Subject: Re: (fractint) FOTD 06-10-01 (Mandelbrot Midget [5]) Date: 06 Oct 2001 20:19:18 +0100 On Sat, 6 Oct 2001 11:04:22 EDT, JimMuth@aol.com wrote: > [cut] >It's now time to start my well-earned week-end. Maybe, if I= try hard enough, I'll manage to get through the entire week-end= without doing any serious work. (Finding fractals is not serious work.)= Until 24 hours from now, when the next FOTD will appear, take= care, and be fractally oriented. Come now, Jim,surely finding fractals _is_ serious work.= Seriously enjoyable work, and something we seriously look forward to= seeing! :-) John -- John Lewis, jlewis@clara.net on 10/06/2001 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 07-10-01 (Hyper-Two [5]) Date: 07 Oct 2001 10:37:55 EDT FOTD -- October 07, 2001 (Rating 5) Fractal visionaries and enthusiasts: There is the original classic Mandelbrot set, which we all are familiar with. And then there are the countless sets which surround the M-set, and are almost exactly like it, but with strange and interesting differences. These sets, which I like to think of as supernumerary, are the sets with exponents of Z such as 2.05 and 1.95. Unlike the classic M-set, these supernumerary sets cannot be displayed on a single screen. In fact they cannot be displayed in their entirety at all, because they are infinite in surface extent. Their actual shape cannot be visualized, since it is hyperdimensional, but it can be approximated by an infinite spiral, somewhat like the blade of a post-hole digger. The closer the exponent of Z lies to the integer 2, the more slowly these supernumerary fractals change as the calculated section of the spiral is removed from the ground level. When the exponent is exactly 2, there is no change at all. In today's fractal, the exponent of Z is 2.05, and the view has been moved 10 -- let's call it revolutions -- up the spiral. The overall shape of the parent fractal closely resembles the classic M-set rotated 45 degrees clockwise, but the distortions are immediately apparent. The main bud, which at this new orientation points northwest, is broken by a spurious valley on its northeast shore. This valley is filled with closely spaced branch cuts and sinuous filaments, on one of which lies today's midget. With a generating formula of Z^(2.05)+C, the midget has *almost* 8 sinuous elements surrounding it, though some of these elements are broken and unevenly spaced. Considering the exponent of 2.05, I named the image "Hyper-Two", and rated it an all-too- easy-to-achieve 5. The parameter file's render time in the 3-minute range makes it not too inconvenient to run, but as always, the ultimate in convenience can be found on the internet at: and at: where Paul and Scott will momentarily post the GIF image ready for download. The fractal weather today (Saturday Oct 6) started with a squall of wind and rain, which caused a brief power outage. By midday however things settled into a partly cloudy, breezy pattern, with a temperature around 60F 15.5C. The fractal cats dislike wind, which covers the signs of approaching danger. They spent the afternoon on their shelf by the window, watching the world go by. Well, it's once again Sunday morning here at Fractal Central. And Sunday is my day of rest. I think I'll rest today by taking a trip to the land of fractals to see what I can find there. If I find anything of interest, it will appear as the next FOTD. Until the next FOTD, take care, and believe what you will. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Hyper-Two { ; time=0:03:21.69--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.26165001846746670/+0.849300872259936\ 60/2.095812e+008/1/-114.999999882607526/-2.1637172\ 242794378e-007 params=2.05/0/10/0 float=y maxiter=1200 inside=0 logmap=92 sound=off colors=000wXutWtrWtoVtmVsjUshUsWQiKM`LQcMTfNXhO_kP\ bnQfpRisRluP_kONaLIPJEDQFJWGOaHUgIZhOUhTPhZKicFiiA\ in5is1gf8eUFcHMa5SiLXq_`xndvhctccsZcqUcoPcnKcYNWHQ\ O0SH9UMIWRRYWZ__5CTDINLOITUD`_8cRAgICj9Em0Gl1Dk2Aj\ 37i44i52l7Ro9omCjlEfkHbjJYiMUhOQgQMbLTYH_UDfP9mL5s\ 1dcAbbJabS_a_ZahX`qW`yV`rWYkXVdYSYZQR_NK`KEaIMWEUQ\ BWRGXRLYRPZRU_RZ`RbaRgbRkeSegT`iUWlVQnWLpXGrXBqaGp\ eLoiQnnVmr_mvdip_ekVbfRZaMVXHSSD`JFiAHr2JcAOPHSBOW\ DPSEPOFPKGQGHQCIQ9qcxhWr`OmSHhK9cC2ZN9cXFhgMmqSqnP\ kkMfhJ`eGWbDQ`ALUpAZiJbbSgW`kPipIrtBzyecqf`jgYbhVW\ iSPjPLiMHiJDhGAhE8lF6pG4tHHvKTxNdyQVnJLdDCV7LO5TH4\ aA3i32zykovWdtGbUbiUgpUlwUqmUrdUsVUtMUuNUoOUjPVdQW\ _RXUSYPQ_VOa_NcdLeiJgnIisMkoQmkUogXqc`s_duWhwSkyOn\ zSqzVszZvzaxzd_zdCzdIzYNzSTzMYzGbzAXzHSzONzVHzaCzh\ 7zoCzjGzfLzaPzYTzUYzPazLezHbzE`zCZz9Xz7Vz4Tz2QzFNz\ RKzcIzoLzfOzYKzRhzpmzrrzt } 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| and at: The fractal weather today was totally fall-like, with blue sky foiled by blustery clouds, and a temperature of 58F 14C, which kept the cats close to the house. I'll end this now, but I'll return in 24 hours with the next FOTD. Until then, take care, and hope for the best. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_NewSeahorseAngle { ; time=0:01:05.91--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=t center-mag=-0.621972/-0.0521346/6.215162/1/180 params=90/86/2/0/0/0/-0.7525/0 float=y maxiter=1800 inside=0 logmap=6 colors=000BV8CU9DSAEQBFOCGNDHLEIJFJHGEBFJGHNKJROKW\ SM_WNc_PhcRlgSpkUrmUtmVslTrjRrgQqeOqbNp`LoYKoWInTH\ nRFmOElMClJBkH9lD4kF8jHBiJEiLIhMLgOOgQSfSVeUYeUZbV\ `cU_XVZYTYTRZPO_LM_GJ`CGa7C`8Ea8Fa9Ga9Ha9IbAJbAKbA\ LbBNcBOcCPcCQcCRdDSdDReDQfDPfAOf9Nf8Mf7Lf6Kf5Jf4Lk\ 3Mo5Kk7Jh9HdBGaDEZFDVHBSJAOL8LN7IP5ER4BV05T38S5BQ7\ EPAHOCKMENLGQJJTILWHNZFPaESdCUgBWjAYmGVfLS`QPVVMPY\ IF_KJ`MMaNPcPTdRWeSZfUahWeiXhjZkk_ni`ohaofaoebodco\ bcoado`eoZeoYfoafrXfoTclO`iPYhPVfPSYPPXNMWLMVINUGP\ UEQTBRS9SR7TRBSSESSHSSKRSNRSQRSTQSWQSYMRZQSZTSZWS_\ _S_dT_gT`fTaeTcdTecMgbGiaFk`Em_DoZCmcBkhAkk6jmAjkE\ jjIjhMjgQjeUjcYjbaj`ej`gjZigWjdSkaNmZJnWFoTAqQ6rO2\ sO6nO9iODdOG_PIROJWNK`NLdLNfKOgJPhHRjGSkFTlEVmCWoB\ XpAZq9_r7`t6bu5cv4dwAcpGcjLccRcYXcSacLgcFlc9ggGcjN\ _mUWp`SsgOvnQveSvXUvOWvFYv6Ww9VwBUwDTwFSwIQxKPxMOx\ ONxRMxTKyVJyXIy_HyaGycFye } frm:multirot-XZ-YW-new {; 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)+p3, c=e*imag(pixel)+p4: z=z^(p2)+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: John Lewis Subject: Re: (fractint) FOTD 08-10-01 (A New Seahorse Angle [4]) Date: 08 Oct 2001 20:08:25 +0100 On Mon, 8 Oct 2001 10:49:17 EDT, JimMuth@aol.com wrote: > >FOTD -- October 08, 2001 (Rating 4) I thought this appealing - I would have raised its rating to 7 at= least. John -- John Lewis, jlewis@clara.net on 10/08/2001 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 09-10-01 (A Fractal in Paradise [9]) Date: 09 Oct 2001 10:04:08 EDT FOTD -- October 09, 2001 (Rating 9) Fractal visionaries and enthusiasts: Today's fractal image is one of those rare ones that rates a 9. But once again I have only a few moments to write about it. The image results from a critical combination of Z, 1/Z and 1/C. I named the picture "A Fractal in Paradise", mostly for whimsical reasons. The rating of 9 is an honest appraisal of the image, which IMO is exceptional. An added bonus is the relatively brief 12-minute render time from the parameter file, though a download of the GIF image from: or: will be even faster. The fractal weather today here at Fractal Central was sunny but brisk, with a temperature of 57F 14C. These conditions pleased the cats, and the cats showed their contentment by sleeping peacefully. Thomas, the oversized yellow-orange one, interrupted his rest long enough to come visit me for a scratching under the chin which he repaid by giving me a brief purr. Tippy, the tabby, having much sleep to catch up on, had no time to get scratched or purr, and slept through the entire afternoon. Even as I write these words, I see work piled on the table across the room, waiting to be done. I'll start by scanning the envelope of photographs. Then, when the day's tasks are completed, I'll boot the fractal computer and return to the world of fractals. Until I reappear in 24 hours, take care, and never surrender hope. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ AFractalInParadise { ; time=0:12:23.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.50122497628874820/+0.027870570081222\ 95/947845/1/-155.000000005278793/1.086948586692670\ 91e-009 params=-1/-1/-1/1/-0.012/2 float=y maxiter=900 inside=0 logmap=260 colors=000rK0lTTlTTlTSlTQlTQmXSoYSp`TraTsdVufVugXv\ jXxlYyoYzp_zs_zu`zvaxubsucoucjscfscascYrcTrcPrcLpc\ GpcCpcFmcIl`LiYOgVPdSScPV`MY_J`WLaVMaRGaRCUS6ZM1YN\ 0YK0YK0dR1fUGgdVijijtxjzzfszamx_irVclQ_fOU`JQVFLPC\ GJ7CD4771C60F40J30O30S10Y00a00f00j00o00c74cIDcSMca\ TcjQUdPc_MQTL_OIiIGrCDz6Cz0Gz6LrCOiGS_MVQS_IXa7af0\ gi0lm0cp6VsDMvMDyT4z`0sX0lS0dO0`P0YQ0VQ0SS0OS0LT0I\ T1FV3AX47X64Y61Y70_90_A0`C0`C0XA0T90Q70M63J46G39C1\ A90D60G10J00M00P00S00T00JQ49zGAzICzICyIDxIFvIFuIGs\ IGrIIpIJoIJmILlILjIMTLOCOP0QQ0SQ0SQ3SQ6SQ7SQASQDSQ\ GSQJSQLSQOSQQSQTSQVSODaM0jQ4cVCYYJQaQLfYFid7ml1pr0\ dAF_C`VCuY9s`6rc4pf1og0mj0lm0jp0ir0il6_fJQ`YGVj7Qx\ 0Tv1Vv4Yv7_v9`vCcvFdvIfvJivMjvPlvQdrM_mJTiFOgCIg7C\ g46g00g04iA7jMClYFmjJovMpzSryXspaugfv``yaXzaQzcMzc\ GzdCzd6zf1zf0zfGzYYzPozGzz9vzIlzQaz_dzXgzVmzipzfoz\ dozcozaozaoz`mz_mzYmzYmzX } 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) FOTD 10-10-01 (Criss-cross Midget [7]) Date: 10 Oct 2001 09:34:37 EDT FOTD -- October 10, 2001 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal continues the same approach as yesterday's -- mixing portions of (Z) and (1/Z). In today's case however, there is a difference. Instead of exactly Z and 1/Z, we subtract some Z^(0.97) from some Z^(-1.15) before adding (1/C). The parent fractal consists of a Mandeloid so distorted that its parts are virtually unrecognizable. It also has a smooth-edged eye-shaped open area extending to the east. Part of the Mandel figure is obscured behind a circular disk at its origin, but a rudimentary valley barely escapes being obscured. Today's scene is located in a cut-off thread of chaos that lies in the northwest branch of this valley. A fitting name for today's image eluded me. There are many themes that could be emphasized. After studying the scene for several minutes, I noticed the eight-armed cross, which could be taken as two four-armed crosses, and named the picture "Criss-cross Midget". It's another above average image, but the rating of 7 falls short of yesterday's superior 9. Unfortunately, today's parameter file takes 44 minutes to render -- at least on my tired 200mhz Pentium machine. A better way of seeing the scene is to give Paul and Scott a chance to render it from the parameter file and download the GIF image from their web sites at: and at: The fractal weather today here at Fractal Central proved ideal. After a frosty start, the warm sun boosted the temperature to 63F 17C, and brought out the fractal cats for a romp in the yard. They somehow managed to keep out of trouble for an entire day. As for me, I'm about ready to start another day's work. With any luck, I'll finish early and have time to find another 9-rated fractal. If not a 9, a 5 or 6 image will do. Until next time, take care, and search for truth wherever it may be found. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Criss-cross_Midget { ; time=0:44:43.00--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.08314704524001394/+0.131224272955765\ 10/1.411807e+010/1/64.9999880445045193/1.014667755\ 64301726e-006 params=0.8/-1.15/-0.9/0.97/0.185/0 float=y maxiter=12000 inside=0 logmap=580 colors=000K5PL5RM5UO5WP5ZQ5`R5cT5eU5hWFjPPdGZY9hRJ\ _LTTFaLAkD4u50z00z00x20u33s46p5An6Dk8GhAKeBMcDQ`EU\ ZFWWG_UIcRJeUJcWJaYJ`_J_`JZcJYdJW`I_YIaUIeQIhMIjJG\ nFGpBGs8Gv4Gy0Gz2Kx2Ou3Qq3Uo4Wk4_i5ae5ec5i_6kY6oU8\ qR8uO9xL9zI9zF8yI6tK5pM5kP4hR3cU2_W2VZ0Q`0Mc0Ie0Eh\ 09j05l00o00q03n69kDFhILeORaUY__cWdiUjoQpuOuzLtxOtu\ QtsRspUsnVskYsi_qh`qecqcdq`fpZipWjpUlpTnoThnTcnTZl\ TUkTOkTJjTEjT9VVTGYk2_z9YuGVkMUaTT`YT_cT_hTZnRYsRY\ yRWzRWzWTx_PtdLqhIokEkpAit6fx3as4Yo5Tk5Oh6Kd6F_8AW\ 95T90PA0LA5KEDJILILTIO`GRhFVpEZxE`qJYlOVhTRcYPY`LT\ eJOjFJoDEsADqEBpIIoLOnPUlT_lVeoakqhqsnxutzxzzyzzvz\ zuzxszqqzkpzenz_lyUkxOjvIkuFluEntBosApq9qp8sp8tj8u\ e8v`8xW8yR8zL8zG8zB8z68z29z69zAAzEAzJAzMBzQBzUBzZD\ zaDzeDziEzjFzjGzkIzkJzlKzlLznMznOzoPzoQzpRzpRzpTzk\ UzfVzaWzZZz_`z_cz_ez_hz`iz`kz`nz`pzaszauzavzalzjdz\ qWzzOzzWzudzdcziaznazq`zv } 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) Fractalus down Date: 11 Oct 2001 01:31:48 -0500 I was wondering why the PhiloFractal posting of Jim's FOTD never showed up this morning so I could create the web page. Finally found out the reason late in the evening from a posting to the Yahoo eGroup: Janet Preslar posted to Fractal-World: > > Damien has asked me to post that the Fractalus server has > had a "catastrophic hardware failure" and will be offline > until sometime Friday. This affects not only the Fractalus > website but all the mailing lists hosted there. He'll be > posting here when everything is up and running again. > 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) FOTD 11-10-01 (Fractal Thursday [6]) Date: 11 Oct 2001 11:38:32 EDT FOTD -- October 11, 2001 (Rating 6) Fractal visionaries and enthusiasts: With the philofractal list down for a couple days, I'm taking advantage of the philosophical time-out to catch up on some humdrum everyday work that has been accumulating the past week or so. When the list comes back online, I'll pontificate with the philosophical pondering I've been doing. In the meantime the fractals keep coming. Today's image features a return to the Mandelbrot set for a view of a midget never before seen. (Almost all deep midgets in the M-set have never been seen.) This time we journey out the negative stem to the fourth valley, the one I call Triple-Scepter Valley. Today's midget lies in a spiral of this fourth valley, a fact that is verified by the abundance of spirals surrounding the midget. I had intended on trying the outside option on this image, but when this option is used, the rendering speed slows down for some reason by a factor of over 20. The normal equal-iteration-bands method of coloring produces an image every bit as worthwhile, which rates an above-average 6. With no immediate ideas for a better name, I named the image "Fractal Thursday". It's a fair description of the time in which the image was found. The parameter file runs in 3 minutes. Paul and Scott will have the image posted to their web sites within the hour. Those web sites can be found at: and at: The fractal weather today was sunny and warm. The temperature of 75F 24C kept the cats out in the yard most all day. When the weather is good and the cats are outside, they are happy cats. Therefore the cats were happy all day. And I'll be a bit happier when I get a bit of this backed-up work finished. So until next time, which will be tomorrow, take care, and the rest will be easy. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= Fractal_Thursday { ; time=0:03:23.01--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.39409909557595400/+0.000621121594793\ 03/2.52296e+009/1/-99.999992975078527/-1.253472398\ 37772517e-005 params=0/0 float=y maxiter=50000 inside=0 logmap=-3425 colors=000fTzhRyiSyjTykUylVymWynXyoYypZxq_xr`xsaxt\ bxucxvdxwexxfxwguwhrvipvjmujjuihtiethbsg`sfYsdVrcT\ rbQqaNq`LpZIpYFoXDoVAmT7iR7eP7aN6ZMBVFCRCCN9DK7EG4\ EEDFFEFGHEIJDJMCLOBMRBOTAPW9RY8S`7Sa7Rc6Rd5Qf4Qg3P\ i3Pj2Ol1Om0On0Ml2Lk3Kj4Ji5Ih6Hg7Gf8Ee9DdACcBBbDAaE\ 9`F8_G6ZH5YI4XJ3WK2VL1UM0TN1VM1WL2XK2YJ2_I3`H3aG3b\ F4cE4eD4fC5gB5hA5j96k86l76m67n57p47q38r28s18t1As2C\ s3Er4Gr5Iq6Kq6Mr7Os8Qt9SuATvAVwBXxCZyD`zEbzFdzFfzG\ hzHjzIlzJmzJkzIjzIizHgzHfzHezGczGbzFazF_zFZzEYzEWz\ DVzDUzDTzFTzGTzITzJTzLTzMTzOSzPSzRSzSSzUSzVSzXSzYR\ z_Rz`RzbRzcRzeRzfRzhRziQznQzsPzaOzLOz4Sz9VzEYzJ`zO\ czSfzXizalzfozkrzosziszdszZszUqzVozVmzWkzWizXgzXez\ YczYazZ_zZYz_Wz_Uz`Sz`Qz`UzaXzb_zcbzdezdozMxz3sz7o\ zAjzEfzHazKYzOTzRPzVKzYGz`IzcJzeKzhLzjMzmOzoPzrQzt\ RzwSzyUzuWzqXzmZzi`zeazaczYezVfzRhzNjzJkzFmzBoz7pz\ 4szuqzrozpmznkzljzjhzgfzy } 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: "Paul N. Lee" Subject: Re: (fractint) FOTD 11-10-01 (Fractal Thursday [6]) Date: 11 Oct 2001 13:47:36 -0500 JimMuth@aol.com wrote: > > When the list comes back online, I'll pontificate > with the philosophical pondering I've been doing. > I noticed that you sent a single copy of the FOTD yesterday, as opposed to a CC'ed version to the Philofractal list. Which means that Wednesday's philosophy may be lost if all recently sent email on Fractalus is gone. 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) Re: FOTD 11-10-01 Date: 11 Oct 2001 15:06:28 EDT Paul Lee wrote: >I noticed that you sent a single copy of the FOTD >yesterday, as opposed to a CC'ed version to the >Philofractal list. Which means that Wednesday's >philosophy may be lost if all recently sent email >on Fractalus is gone. No problem. I've got the missing philosophy on hold and I'll post it when the philofractal list comes back online. 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) FOTD 12-10-01 (Fractal Flinders [6]) Date: 11 Oct 2001 22:42:15 EDT FOTD -- October 12, 2001 (Rating 6) Fractal visionaries and enthusiasts: Sometimes, perfectly good fractals turn into a mass of bits and pieces -- flinders that is -- and today's image is a perfect example of this fractal disintegration. I started with a perfectly good fractal -- the figure created by the formula Z^1.5874+C (the 1-1/2 root of 2) -- and investigated the area 6 levels up the logarithmic spiral. I chose a perfectly ordinary appearing valley to delve into, but I had not gone far when the whole fractal world disintegrated around me. Such disintegration usually signals a dead end of the search. Not in today's case however. This left-over chaos is filled with debris, which in itself forms recognizable repeating patterns. And as an added attraction, the chaos is overflowing with deficient midgets of all sizes and shapes. The overall effect of the image is one of fractal flinders floating in a vast space near a relatively unimpressive midget. The pieces almost appear to be drawn down into the midget as though it were a black hole. I first thought of naming the image "Black Hole", but decided on "Fractal Flinders", a title with a more attractive sound. The 16-minute render time will leave some impatient. The 1-minute download of the finished GIF image from the W.W.Web at: or at: will be far more satisfying for these impatient ones. The fractal weather today featured blue skies, puffy cumulus clouds, gentle breezes, and a temperature of 79F 26C. All in all it was a perfect Autumn day, which left the fractal cats purring with contentment. No philosophy will be lost while the philofractal list is down. I'm still writing my thoughts, and saving them in a separate file. The accumulated wisdom will appear as soon as the philofractal list is once again up and running. That's it for today, fractal fans. It's time to shut down the fractal shoppe and call it an evening. But the next FOTD will appear in two wags of a . . . a pussy cat's tail. Until then, take care, and I have not yet begun to explore. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fractal_Flinders { ; time=0:16:31.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.51849225088358700/-0.546491304449809\ /24561.24 params=1.5874/0/6/0 float=y maxiter=36000 inside=0 logmap=254 colors=000_Q0`R0`S0_R0ZQ0WP0VN0UN0SM0QL0PK0NI0MH0L\ H0KG0i_lfDidHkdKkdNlcQlcUmcWmc_nbbnbepbhpbkp`cb`WQ\ _PC_I0PD5F8C35I05NQbmNZgMWbKUWIQRHNMFLGDHAAE49C089\ 07D07F05K05M24Q44S53W83Z92bA2dD0hF0kH0nI0qL0uM0wN4\ qSAkYHebM_gSUlZPqdIviDzlEwmEvpEtqErtEpuEnwElyEkzEh\ zEgzEfyH`tIYnKUkMQfNM`PIWRFSSANU7IW3DX09Z09Z08Z0CZ\ 0HQ0KQ0MR0PR0RS0UU0WU0ZV0bW0fW2lW2rW3KVELVGLVIMVKN\ VMNVOPUQQUSRUURUWSUYUS_USaVScWSeYSgYSiZRk_Rm_Rm`Rm\ bRmbRmcQmdQmfQmfQmgQmhPmhPmiPmkPmlPmlPmmNmnNnnNopN\ pqNqqNrrMstMtuMuuMvvMwwLwwLwyLwzLwzLwzLwzKwzKwzKwz\ KwzKwzKwzLwzLwzMwzMwzNwzNwyPwwPxwPyvQzuQztRztRzrSz\ qSzpUzpUznUzmVzlVzlWzkWziXzhXzhXzgZzfZzd_zd_zc`zb`\ z`bz`bz_bzZczYczYdzWdzVezUezUezUdzUdzUczUczUczUbzU\ bzUbzU`zU`zU`zU_zU_zUZzUZzUZzUXzUXzUXzUWzUWzUWzUVz\ UVzUUzUUzUUzUSzUSzUSzURzURzURzUQzUQzUPzUPzUPzUNzUN\ zUNzUMzUMzUMzUMzUMzUMzUMz } 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| or at: and pick up the image from there. The fractal weather today (Oct 12) was ideal, with blue skies, puffy clouds, and a cat-pleasing temperature of 77F 25C. More of the same is expected this afternoon. When I last checked, the philofractal list was still down, so the philosophy will be held for at least one more day. Until next time, take care, and be up and running. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= V_For_Victory { ; time=0:01:10.46--SF5 on a P200 reset=2002 type=mandel passes=b mathtolerance=/1 center-mag=+0.28174961344731050/-0.009596893105776\ 96/1.528115e+013/1/-117.488176390760771/-0.0292145\ 165871739859 params=0/0 float=y maxiter=18000 bailout=6 inside=255 logmap=1637 colors=000nl0rk0of0lc0i`1fY1cT3`Q4YN4VK6SG7PD7MA9J\ 7AG3AD0CA0D70D0VX0zn0zg0zc0z_3zV7zQAzM9wP9tS9pT7lX\ 7i_7f`7cc6_f6Xg6Tk6Ql9MiCJfDGcGD`J9YK6VN3SQ0PS0MV0\ JY0G_0Ed0Kk0Qp0Xw1az4gz7nzAtz9pz9nz9kx7gt7dp7al7_i\ 6Xd6Ta6QY4NV4KQ4HN4GX1Ed0Dn0Cw0Az09x0Dr0Gl0Kf0N`0Q\ V0VP1YJ3aD4d76g17l09o0Ar_0i`0fa1dc3ad3`f4_g6Xi7Vk7\ Tl9QnAPoCMpCKrDJtEGvGEvGDnJKfMQ_NXTQaMSgEVn9XtK`iV\ d`fgQplHzp7zt0pt9VtJ9tTEnSKgQQaPXYNaSMgMKnGJrCJrDG\ rEEtGCvHAvJ7vK6vK4vJ6vJ6vH6vH6vCMv7`n1pn0zf0xf1rf3\ lf4ff6`f7VfAPfCJfDDcE7cG1dH0fJ0cH0aH0`H3YH7XGCVGGS\ GKQGPPETMEfKEnJEvGDzDDvADg7Dg4Dg1Dg0Dg0Dg0Dg0Hn7Kr\ ENwKQzSTz_Xzd_zcYzcXzcVzcTwaSraQoaPpaNraMt`Kv`Jw`H\ x`Gz`EzdDzgDzlCzoCziEzdGz`HzXKzQMzMNzHQzDSz7Sz3Sz0\ Sz0SzGSzKSzQSzXSz`SzfKzk9zp0zv0zt0zr0zp0zo0zk1zg4z\ d9zaCzYEzVJzSMzPPzMTzHXzE_zCcz9fz6izKGzY0zzKzxNzxP\ zxQzxTzxVzxXzx_zYpzaozzzz } END 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: Jim Muth Subject: (fractint) FOTD 14-10-01 (Fracler [8]) Date: 14 Oct 2001 10:16:57 -0400 (EDT) FOTD -- October 14, 2001 (Rating 8) Fractal visionaries and enthusiasts: When today's parameters are entered into the MandelbrotMix4 formula, the resulting fractal looks like a snail with its head out of its shell, facing east. Today's image is located in a narrow cleft of disconnected chaos near the edge of the back of the snail's neck. Actually, today's midget lies in the northern suburbs of a larger midget in the area. The larger midget, which is a less spectacular version of the midget in today's image, can be seen by resetting the log palette to zero and backing out three zooms. The generating formula subtracts 1.4 parts of Z^(-1.17) from 1.4 parts of Z^(0.87), then adds (1/C) to create the parent fractal snail. The image itself reminds me of an alien flower, thus the name "Fractal Flower", which I shortened to "Fracler". Since I think the image is quite good, I rated it at an exceptional 8. Others may have a different opinion. On my worn-out but still eager Pentium 200mhz machine, the parameter file renders in just under 13 minutes. Much time can be saved by picking up the GIF image from the W.W.Web at: or at: With blue skies, puffy white cumulus clouds, and a temperature of 79F 26C, the fractal weather today here at Fractal Central was once again perfect. And the cats must have agreed, because they spent most of the day in the outdoor world. To add to the excitement, Tippy, the active one, actually caught a mouse and brought it to the door to show me. The mouse appeared to be unharmed, so after praising Tippy, I took the mouse and returned it to the yard. As it scampered away, I warned it to be more alert for predator cats the next time. The philosophy is accumulating while the philofractal list, having suffered a 'catastrophic' failure, (reminds me of the WTC), remains down. When, and now I'm beginning to wonder if, the list once again becomes operational, I'll have lots of controversial philosophy to share. Until then, the fractals will continue appearing at a rate of one per day on the Fractint list, together with lots of fractal talk, but little philosophy. The next fractal will appear right here in about 24 hours. Take care, and when the going gets tough . . . what *do* the tough do? Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fracler { ; time=0:12:53.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.039444410280139/+0.71916981442691810\ /5.739517e+007/1/-137.499999948393366/1.5697518258\ 1675643e-007 params=-1.4/-1.17/1.4/0.87/0/5 float=y maxiter=2500 inside=0 logmap=253 periodicity=25 colors=000Q0WS0UT0SU0PV0NW0KY0J_0Na1Qc2Ud4Ye5ah6di\ 8hj9kmAonBsoCvmEtkFsjGriIphJogKmeLkcLjbNi1EO5GP8IP\ AJQEKQGLQJNSNOSVPTSQTUPTUOJTNJGL9KL8NO8PR6TT6VW5YZ\ 5aa4cd4eg2ii2kk1no1rr0tt0vv0tn5sgAp_FoTKmLPkEUj6ZP\ Ld2V6TV6pQVpTVpUWpUGpU0sP0tL0vI0wK0yN0zP0zS0zU0zV0\ zY0za0zZ0zW0zU0zS0yP0vN0uK0sI0pF0oC0mA0kB0iC0hC0dB\ 0aA0Y90U80Q60N50J40F20B10800400000211542852A84C94F\ B5IC5KF6NG6PJ8SK8UN9WO9ZQA_SAaQ8aQ5bQ2bQ1cQ0cQ0cQ0\ eP0gO2hN5iL9jKCkJFmIJnGLpFPrETsCVtBZuAbv9dw8hy6jv9\ htBgsCdpFcnIamJ_jLYhOWgPUdSTbUQaVPaVOaVOV_YPeeSaeU\ YeVTeYPe_KdbGdcBde8dh2di0db2YW5SQ8LKBEEE88G11J0NVA\ egPyscvrburasparp_ppZnoZmoYkoYUSmB4zNAzWGyeLwoSvyY\ uzbttchecYScLEcAehZzmuzksujrojojinehk_hjVghQigKkdF\ ncApa4s_0uY0wW5zYGzYSzZbzZmz_wz_zz_zzbyzcuzdrzenzg\ ozcpz_pzWrzTrzPQzZ0zhzzCyzFpzIhzK_zNTzOKzQBzT2zV0z\ W4zLCzAKz0LzELzSLzcOzaPzZ } 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: Re: (fractint) FOTD 13-10-01 (V For Victory [5]) Date: 15 Oct 2001 13:08:05 +0000 >Unsure of how to rate the image, and following the principle of >'when in doubt, make it average', I settled on a rating of a >generic 5, though a 6 would also be reasonably close. I always >tend to under-rate images in the classic M-set. They seem to >come just a bit too easily. I rate images (and music, for that matter...) by how good the end result is, not how easy or otherwise it was to create. By my scale, this image should rate nearer 8, if only for the cool colour scheme. Thanks. Andrew. _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp 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) FOTD 14-10-01 (Fracler [8]) Date: 15 Oct 2001 13:11:43 +0000 >From: Jim Muth >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >Subject: (fractint) FOTD 14-10-01 (Fracler [8]) >Date: Sun, 14 Oct 2001 10:16:57 -0400 (EDT) > > >FOTD -- October 14, 2001 (Rating 8) > >Fractal visionaries and enthusiasts: > >The generating formula subtracts 1.4 parts of Z^(-1.17) from 1.4 >parts of Z^(0.87), then adds (1/C) to create the parent fractal >snail. The image itself reminds me of an alien flower, thus the >name "Fractal Flower", which I shortened to "Fracler". Since I >think the image is quite good, I rated it at an exceptional 8. >Others may have a different opinion. I for one agree with that particular rating. (If I thing an image is over-rated, I generally don't bother to post a message saying so. I guess I'm just NICE or something...) THanks. AnDRew. _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp 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) FOTD 15-10-01 (Fractal Bagel [5]) Date: 15 Oct 2001 09:20:43 -0400 (EDT) FOTD -- October 15, 2001 (Rating 5) Fractal visionaries and enthusiasts: Fractals are total abstractions. There is no 'real' Mandelbrot set or Julia sets lurking in as-yet-undiscovered hiding places. It is all about numbers and the things numbers do. But we are a part of reality and cannot escape it. Our minds are wired to see 'real' objects even where none exist. Perhaps the strongest evidence of this wiring is the way we so often invent then actually see faces in random patterns such as clouds. I could find no face in today's image, though I did find a bagel. In fact, the whole scene is of one big bagel, which is why I named the image "Fractal Bagel". The midget lies in a chaotic filament on the northwest border of the fractal that results when the expression Z^1.44225+C is iterated by the MandelbrotBC1 formula, using the function. I chose the value 1.44225 as the exponent of Z because it is the cube root of 3, and whole-number roots of whole numbers seem to make more interesting images. The rating of 5 is average, and says nothing about the image. The proper function to use with the MandelbrotBC1 formula is , but most other functions also produce interesting fractals. In today's case I used the function to see what it would do. On my machine, the parameter file takes over 1/2 hour to run. But my machine is old and tired, and most machines will render the image in less than 15 minutes. Those who would rather do no rendering at all can find the GIF image posted to the W.W.Web at: and at: The fractal weather today (Sunday) suffered a setback, with only a few brief periods of sun and too much wind for the sensitive fractal cats. The temperature of 75F 24C was pleasant enough, but the wind limited the cats to a couple brief outings. A heavy shower fell after dark, bringing a less-than-perfect end to the inauspicious day, but by this time, the cats had long since given up and settled into the world of sleep. The philofractal list is still down, so the philosophy is still in cold storage. And I'm hot to get the day's work started. Until next fractal, take care, and fractals are real because we see them, but are they really real. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fractal_Bagel { ; time=0:34:17.78--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-1.08717603028377500/+1.205061829294592\ 00/1.889778e+011/1/42.4995365922868444/-0.00193853\ 530842458266 params=1.44225/0/0/0 float=y maxiter=45000 inside=0 colors=000ebHfcFgcEhdDieCjfBkfAlg9mh8ni7oi6nj7nj8n\ j9njAnjBmjCmjDmjEmjFmjGmjHlkIlkJlkKlkLlkMlkNkkOkkP\ kkQkkRkkSkkTjlUjlVjlWjlXjlYjlZil_il`ilailbilcgpjil\ dji_lfVmcPo`KpYFqVAbFDO0GQ1HR2HS3IT4IU5JV6JW7KX8KZ\ 9K_AL`BLaCMbCMcDNdENeFOgGOhHOiIPjJPkKQlLQmMRnNRmIT\ oNRpSQrXPsaNufMvkLxpJyuIzyHywIxvIwtIvsIuqItpJsoJsm\ JrlJqjJpiKogKnfKmeKlcKlbLk`Lj_LiZLhXLgWMfUMeTMeRMd\ QMbPN`NNZMNXKNVJNVJMTINSIORIOQHPQHPQHQQGQQGRQGRRFS\ SFTTFTUEUVEUWEVWEVVDWWDWWDXWCXXCYXCZXBZYB_YB_XA`XA\ `XAaXAaX9bX9bX9cX8dW8dW8eW7eW7fW7fW6gW6gW6hY4gW6hV\ 7iU9jSAjRBkQDlPEmNFmMHnLIoKKpILpHMqGOrFPsDQsCStBTu\ AUuCRtEPsGNrIKqKIpMGoODoNEnNFnNGnNGnNHnNImNImNJmNK\ mNKmMLlMMlMMlMNlMOlMOkMPkMQkMQkMRkLSjLSjLTjLUjLUjL\ ViLWiLWiLXiLYiKYhKZhK_hK_hK`hKagKagKbgKcgLdhKcgJcf\ IbeHbdGbcGabFaaEa`D`_C`ZB`YB_XA_W9_V8ZU7ZT6ZS6YR5Y\ Q4YP3XO2XN2XMa_Lb`Kc`JdaI } 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) FOTD 16-10-01 (New Eastern Angle [7]) Date: 16 Oct 2001 09:59:45 -0400 (EDT) FOTD -- October 16, 2001 (Rating 7) Fractal visionaries and enthusiasts: The well-known Mandelbrot set is actually a slice through the center of a less-known four-dimensional object known to Fractint users as the 'Julibrot'. Since the Julibrot is four-dimensional, the M-set does not cut the Julibrot in half, but it does slice a two-dimensional hole all the way through it. All the 'perturbed' M-sets are parallel to the 'true' set, and taken as a single unit, form the Julibrot. The many Julia sets are also slices through the Julibrot. The 2-D Julia sets also cut the 4-D Julibrot in parallel slices, and when taken as a single unit, form the same Julibrot. The difference between the Julia sets and the Mandelbrot sets is the direction in which they cut the 4-D Julibrot. The Julia sets are oriented in a direction completely perpendicular to the Mandelbrot sets. This relation is not the same as that of perpendicular planes in normal 3-space, such as a wall and ceiling, which must always intersect in a line and have common sets of parallel lines. In the 4-D Julibrot, M-sets and J-sets intersect in only a single point, and every line in every M-set is perpendicular to every line in its intersecting J-set. Just as M-sets and J-sets are slices in different directions through the same four-dimensional Julibrot object, there are many other directions in which this 4-D object may be sliced. Today's 7-rated image, which I have named "New Eastern Angle" shows East Valley of the M-set sliced in one of these new directions. Since the slice is in a new direction, there are no Mandelbrot elephants, buds, or brain-like Julia sets to be seen. What is visible is totally unlike any M-set or J-set, and must be seen to be appreciated. The image can be seen by running the attached parameter file or by picking it up from the W.W.Web. The parameter file runs in exactly 7 minutes on my worn-out Pentium 200mhz machine with a noisy fan. Most of the 7 minute render time is spent on the bottom 1/2 inch of the image. The pre-rendered GIF image downloads in even less time from the W.W.Web at: or at: But before going for the download, give Paul and Scott a chance to render and post the image. The fractal weather today here at Fractal Central was once again perfect, with sunny skies and a temperature of 71F 21.5C. The fractal cats agreed, and showed their pleasure by spending most of the afternoon lurking in the yard, watching the squirrels, who are busy gathering their nuts for the coming Winter. Seeing no signs of life yet from fractalus.com, I once again filed away the day's philosophy until and if fractalus has a resurrection. It's now time to file away the fractals and turn to more profitable but less enjoyable activities. Until tomorrow, take care, and be sharp. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ New_Eastern_Angle { ; time=0:07:00.73--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.60570814332461560/+0.250416550291830\ 40/8155.282/0.0003492 params=0/57/2/0/0/0/0/1e-005 float=y maxiter=45000 inside=0 logmap=135 colors=000SUhTUiUUjVUkWUlXUmYUnZUo_Up`UqaUrbUsbUtb\ UucUvdUwdVwdWwdXwcYwcZwc_wc`wbawbbwbcwbdwaexafxagx\ ahx`gx_fwZevYduYcsXcrWbqVapU`oU_mT_lSZkRYjRXhQWgPW\ fOVeNUdNTbMSaLS`KR_KQYJPXIOWHOVGNUGMSFLREKQDKPDJNC\ IMBHLAGK9GJ9FH8EG7DF6CE5AC6CD7DE8FE9GFAIFBJGCKGDMH\ ENHFPIGQIHRJITJJUKKWKLXLMYMN_MO`NPbNQcORdOSfPTgPUi\ QVjQWkRXmRYnSZpS_qT_rTZqQYqOYqMXpJWpHWpFVnFUlFTjGS\ iGRgGQeGOcHOaHP`HQZIRXISVITUIUSJUQJTOJSMKRLKQJKPHK\ OFLNDLMCLLAMK8MJ6MI5MHD8GD8FE9EF9DF9DG9EG9FH9GI9HI\ 9IJ9JJ9KKALKAMKANKAOKAPKAQKARKASKATKAUKBUKBUKBUKBU\ KBUKBUKBUKBUKBUKBUKDUKEUKFUKGUJHUHIUEJUCKUALU7MU5N\ U3OU1PU4OU6OU8OUAOUDNUFNUHNUJNUKMUKMUKMUKMUKNUKNUK\ OUKOUKPUKPUKQUKQUKRUKRUKSUKSUKTUKTUKUUKUUKVUKVUKWU\ KWUKVUKVUKVUKVUJUUFUUBUU8UUCSUFQUIOUKNUKLUKJUKIUKG\ UKEUKDUKBUK9UK8UK9UKAUKBUKCUKDUKEUKFUKGUKHUKIUKJUK\ KUKLUKMUKNUKOUKPUKQUKRUKS } frm:multirot-XZ-YW-new {; 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)+p3, c=e*imag(pixel)+p4: z=z^(p2)+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" -------