From: John R Goering Subject: Re: (fractint) FOTD 01-08-00 (Seahorse Valley [5]) Date: 01 Aug 2000 22:28:27 -0400 On Mon, 31 Jul 2000 22:23:41 -0400 (EDT) Jim Muth writes: > The formula that drew the image and will draw many more FOTD's > this month of August was posted to the Fractint list last July > by John Goering. It is the only formula that draws all possible > oblique angles through the 4-D Julibrot. John Goering responds: While this formula is able to slice the 4-D Julibrot at many different angles (including slices that are parallel to each of the six coordinate planes), unfortunately, I have not proven that it can slice at all possible angles. 4-D space is much more "vast" than 3-D space, and it is difficult (maybe impossible for us mortals?) to visualize complex rotations in that space. When I developed the SliceJB formula, I despaired of ever understanding what goes on when a plane is rotated in 4-D. So I did all of the math work using rotations in 2-D. Since I took this simpler approach, I suspect that this formula cannot produce all possible orientations in 4-D. Thank you, Jim Muth, for the fantastic pictures that you have been producing. Yours truly, John Goering View a Mandelbrot set image gallery at http://homestead.juno.com/johnrhg/files/IntroMandelbrot.html John Ralph H. Goering johnrhg@juno.com Jesus says, "Behold, I am coming soon!" (Revelation 22:12, NIV) ________________________________________________________________ YOU'RE PAYING TOO MUCH FOR THE INTERNET! Juno now offers FREE Internet Access! Try it today - there's no risk! For your FREE software, visit: http://dl.www.juno.com/get/tagj. 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 02-08-00, (The Wrong Way Fractal [5]) Date: 02 Aug 2000 00:38:58 EDT FOTD -- August 02, 2000 (Rating 5) Fractal visionaries and enthusiasts: Despite the latest flooding of the fractal basement, I managed to find a Fractal of the Day this afternoon. The image is a picture of a fairly typical midget in the southern branch of Seahorse Valley at the coordinates -0.7751187297-0.1232311722i. Why then does it not look like a midget? The reason is simple. We are viewing it from the wrong direction. Today's FOTD image is not a scene in the Mandelbrot set, nor is it a scene in a Julia set. It is a hybrid, an Oblate set determined by real(z) and imag(c), with Mandelbrot characteristics in the vertical direction and Julia characteris- tics in the horizontal direction. The name "Oblate" for the images sliced in this direction is of my own invention. The familiar Seahorse Valley features are there, but when seen from this odd direction, they are distorted almost beyond recognition. Also in the image is one of those narrow, straight features that I call bridges. It crosses near the top of the open area. At six minutes, the parameter file is relatively fast by recent standards. The download of the GIF image is even faster however, and may be found by going to the Usenet binary group: or to Paul Lee's web site at: The fractal weather was partly cloudy and sultry today, with a temperature of 86F (30C). Two thunder-storms passed over in the afternoon, with rain so heavy that it looked like fog. The first started the flooding in the basement, the second finished the job. I have had it with water in the basement. I'm now going to relax and let the water go back down the same drain where it comes in, by itself, and do no more mud mopping until the monsoon season ends. The problem is a too-small storm drain, which backs up in excessive rainfalls. The city already knows about the situation and will replace the drain within 5 years or so, as soon as they solve the crime problem. Until then, they tell me it's God's fault for sending such rain. Meanwhile, the fractal cats are complaining about the rain also. Sorry philosophy-starved readers, there is no philosophy today unless you consider a wet basement philosophical. With even heavier rain due tomorrow, we'll probably have no philosophy then either. Until next time, take care, and whistle while you work. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ TheWrongWayFractal { ; time=0:06:33.81 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=slices.frm formulaname=Oblate passes=1 periodicity=0 center-mag=0/0/513184.1/0.2883/0/78.728 params=-0.7751187297/-0.1232318731/-0.7751185803/-0.\ 1232311722 float=y maxiter=12000 inside=0 logmap=277 colors=000VG0VG0WH0<3>_L7`M8aNA<13>cZZdZ_d_ad`cdaeda\ fdaf<2>NSfHOfCMhBLiAJlBKlCKnCKpDKpDLq<11>KNaLN_LOZ<2\ >NOVNOUMSWLVYLWZLYZfBWcFV<3>TSTQVTNYS<3>CjQAnQ7qP4tP\ 2wP<5>Eh_Gf`Icb<3>PWiRUkTSl<3>`HsbFucDv<3>VDdTD_RDWR\ BT<8>FQQERQDTQ<2>9XP8ZP5`L<3>AZ`BYdCYhDYlDQZDJLBD8<1\ 6>hC6jC6lC6<3>sC6<16>rTYrUZrV`rWbrXcrYerYerYfqU`nQW<\ 3>cAK`5HY5EV4BT48SBYRIcVMcZPg<3>maC<6>ddPceRaeS<3>Zg\ `<8>RlMQlLPmJOmI<2>LoDNo8<6>BsW9sZ7ta<2>2uk1vn2vm<4>\ 4yh4yg5zf<2>6zc6zc8zZ<2>EzM } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) FOTD 01-08-00 (Seahorse Valley [5]) Date: 02 Aug 2000 17:34:52 +1200 At 22:28 01/08/2000 -0400, John Goering wrote: >On Mon, 31 Jul 2000 22:23:41 -0400 (EDT) Jim Muth >writes: > > > The formula that drew the image and will draw many more FOTD's > > this month of August was posted to the Fractint list last July > > by John Goering. It is the only formula that draws all possible > > oblique angles through the 4-D Julibrot. > >John Goering responds: > >While this formula is able to slice the 4-D Julibrot at many different >angles (including slices that are parallel to each of the six coordinate >planes), unfortunately, I have not proven that it can slice at all >possible angles. 4-D space is much more "vast" than 3-D space, and it is >difficult (maybe impossible for us mortals?) to visualize complex >rotations in that space. > >When I developed the SliceJB formula, I despaired of ever understanding >what goes on when a plane is rotated in 4-D. So I did all of the math >work using rotations in 2-D. Since I took this simpler approach, I >suspect that this formula cannot produce all possible orientations in >4-D. When you originally posted the SliceJB formula, you offered to post your derivation of the formula also. Perhaps if you did so some of us could check your reasoning and see whether your suspicions are justified. (Alternatively, if you don't reckon it's of general interest, you could just email me privately.) Morgan L. Owens "There are only six real parameters to play with -- enough?" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) FOTD 01-08-00 (Seahorse Valley [5]) Date: 02 Aug 2000 17:31:33 +1200 At 22:28 01/08/2000 -0400, you wrote: >On Mon, 31 Jul 2000 22:23:41 -0400 (EDT) Jim Muth >writes: > > > The formula that drew the image and will draw many more FOTD's > > this month of August was posted to the Fractint list last July > > by John Goering. It is the only formula that draws all possible > > oblique angles through the 4-D Julibrot. > >John Goering responds: > >While this formula is able to slice the 4-D Julibrot at many different >angles (including slices that are parallel to each of the six coordinate >planes), unfortunately, I have not proven that it can slice at all >possible angles. 4-D space is much more "vast" than 3-D space, and it is >difficult (maybe impossible for us mortals?) to visualize complex >rotations in that space. When you originally posted SliceJB, you offered to post your derivation of the formula. Perhaps if you did so we could have a look to see how you pulled it off (and whether you succeeded)? Morgan L. Owens "Many mathematicians write as if the answer emerged fully-fledged Minerva-like from their head." 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 20-07-00 (A Eutectic Mixture [9]) Date: 02 Aug 2000 12:45:01 GMT >From: Jim Muth >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >CC: philofractal@lists.fractalus.com >Subject: (fractint) FOTD 20-07-00 (A Eutectic Mixture [9]) >Date: Wed, 19 Jul 2000 23:55:51 -0400 (EDT) > > >FOTD -- July 20, 2000 (Rating 9) > >Fractal visionaries and enthusiasts: > >No, there is no mistake. Today's FOTD actually rates a 9 -- at >least in my opinion. I am in compleate agreement. >I almost gave a >rating of 9 to yesterday's FOTD, but now I'm glad that I settled >for the 8, since today's picture is notably better and well >worth the 9. Right you are! >I gave the coloring of today's image the extra effort that I >failed to give yesterday's picture, and that extra effort made >the difference, as both underlying images have about the same >potential. Some of the best colouring I've seen for a while! Keep up the good work! (I'm still wading through several weeks worth of emails here!) ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) FOTD 27-07-00 (Lotus [4]) Date: 02 Aug 2000 12:54:25 GMT >From: Jim Muth >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >CC: philofractal@lists.fractalus.com >Subject: (fractint) FOTD 27-07-00 (Lotus [4]) >Date: Thu, 27 Jul 2000 00:02:32 -0400 (EDT) > > >FOTD -- July 27, 2000 (Rating 4) Hmmm... I would have rated it a bit higher... I think it's very pretty! (*still* catching up with me email...) ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) FOTD 30-07-00 (An All-New Midget [6]) Date: 02 Aug 2000 13:00:56 GMT >From: Jim Muth >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >CC: philofractal@lists.fractalus.com >Subject: (fractint) FOTD 30-07-00 (An All-New Midget [6]) >Date: Sat, 29 Jul 2000 22:21:08 -0400 (EDT) > > >FOTD -- July 30, 2000 (Rating 6) Very unusual. I like the combination of purple and green. Very nice! (Only 200 emails to go now...) ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Branch Cuts & Julibrot Slices Date: 02 Aug 2000 13:13:36 GMT Hmmm... I've been doing some work with a little program called "gifcon". I've been animating my "branch cuts" formula... Very cool stuff! I'd show you all... but the files a rather large. But anyway... I wonder if Jim has tried animating Julibrot slices? What does it look like to take a Mandelbrot zoom, and animate it rotating into the Julia plane? Surely that's gotta look pretty increadible, right? Hmm... will try... BTW, I've been thinking about trying to take a sequence of branch cut frames and actually construct a 3D model of the complex exp corkscrew... Take the frames, layer them, and remove the pixels that stay the same colour... I'll let you know if it works! ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: John R Goering Subject: Fw: Re: (fractint) Re: 2D slices of Julibrot Date: 02 Aug 2000 16:00:34 -0400 Here is the post that I sent some time ago concerning the derivation of the SliceJB formula (with some slight changes): Hello to all, Here is the mathematical derivation of the formula that I posted: #1 First, I created the following parameterization of a plane in pqrs-space: p=u, q=v, r=0, and s=0 (where the u-axis is the horizontal axis on the screen and the v-axis is the vertical axis). (In my thinking, I oriented the Julibrot so that the Mandelbrot set is in the pq-plane and the simplest Julia set [the disk] is in the rs-plane) Then I did a sequence of counterclockwise rotations in the following planes: qs-plane, qr-plane, pr-plane, pq-plane. I performed these rotations using the following general formula for performing a rotation in some xy-plane by some angle t: [where the point (xold, yold) is rotated about the origin to the point (xnew, ynew)] #2 xnew=xold*cos(t) - yold*sin(t) ynew=xold*sin(t) + yold*cos(t) First, the rotation in the qs-plane (where a is the angle of rotation): #3 q=v*cos(a) - 0*sin(a) s=v*sin(a) + 0*cos(a) (Note that qold=v and sold=0 [see #2] according to the first parameterization [see #1]. This rotation creates a new parameterization for q and s.) So now the complete parameterization of the uv-plane in pqrs-space is: #4 p=u q=v*cos(a) r=0 s=v*sin(a) Then the rotation in the qr-plane (where b is the angle of rotation and where I substitute the "old" values for q and r from the above parameterization (#4) into the rotation equations (#2)): q=[v*cos(a)]*cos(b) - 0*sin(b) r=[v*cos(a)]*sin(b) + 0*cos(b) The new parameterization in pqrs-space then is: p=u q=v*cos(a)*cos(b) r=v*cos(a)*sin(b) s=v*sin(a) Then the rotation in the pr-plane (where g is the angle of rotation [if you wonder where this sequence of letters is from, I originally used the first 4 letters of the Greek alphabet as the angles of rotation]): p=u*cos(g) - [v*cos(a)*sin(b)]*sin(g) r=u*sin(g) + [v*cos(a)*sin(b)]*cos(g) So the new parameterization in pqrs-space is: p=u*cos(g) - v*cos(a)*sin(b)*sin(g) q=v*cos(a)*cos(b) r=u*sin(g) + v*cos(a)*sin(b)*cos(g) s=v*sin(a) Then the rotation in the pq-plane (where d is the angle of rotation): p=[u*cos(g) - v*cos(a)*sin(b)*sin(g)]*cos(d) - [v*cos(a)*cos(b)]*sin(d) q=[u*cos(g) - v*cos(a)*sin(b)*sin(g)]*sin(d) + [v*cos(a)*cos(b)]*cos(d) After some mathematical manipulations, the complete parameterization is: p=u*cos(g)*cos(d) - v*[cos(a)*sin(b)*sin(g)*cos(d) + cos(a)*cos(b)*sin(d)] q=u*cos(g)*sin(d) + v*[cos(a)*cos(b)*cos(d) - cos(a)*sin(b)*sin(g)*sin(d)] r=u*sin(g) + v*cos(a)*sin(b)*cos(g) s=v*sin(a) Then I performed a simple shift of the origin of the uv-plane to the point (real(p3), imag(p3), 0 ,0). This point is in the pq-plane ( the plane that the M-set is in). So, theoretically, the resulting parameterizations of p and q are: p=u*cos(g)*cos(d) - v*[cos(a)*sin(b)*sin(g)*cos(d) + cos(a)*cos(b)*sin(d)] + real(p3) q=u*cos(g)*sin(d) + v*[cos(a)*cos(b)*cos(d) - cos(a)*sin(b)*sin(g)*sin(d)] + imag(p3) However, to simplify things, I did not really add real(p3) and imag(p3) in the formula until I initialized the value of c So in implementing the parameterization, I initially set z = r + s*i and c = p + q*i + p3 (where p3 is the third parameter. Note that this adds the real portion of p3 to p and the imaginary portion of p3 to q.) I included the formula below so that you can compare the parameterization with how I wrote it in the actual code. SliceJB {; by John R. H. Goering, July 1999 ;This formula produces 2D slices of the 4D Julibrot set. The numbers for ;p1 and p2 describe the rotation of the plane that slices the set (I ;call that plane the uv-plane -- the u-axis is the horizontal axis on ;the screen and the v-axis is the vertical axis). I call the 4 axes ;in 4-space the p, q, r, & s axes. The M-set is in the pq-plane and the ;J-sets are in the rs-plane and planes "parallel" to it. The rotation angles ;are to be entered as fractions of pi (e.g., pi/4 would be entered as 0.25). ;At first, the uv-plane is identical to the pq-plane. ;Then the rotations are performed counterclockwise in each plane as follows: ;First: real(p1)--the rotation in the qs-plane. Then imag(p1)--qr-plane. ;real(p2)--pr-plane. imag(p2)--pq-plane. ;The origin of the resulting skewed uv-plane is then placed at the point ;(real(p3), imag(p3), 0, 0) in pqrs-space. To create the M-set, leave the ;parameters alone, or you may change p3 to change the position of the M-set ;on the uv-plane. ;To create a J-set, set real(p1)=real(p2)=0.5, then set p3 equal to the ;constant for the J-set (let imag(p1)=imag(p2)=0). ;The parameters for p1 and p2 that are needed to put the uv-plane parallel to ;the various coordinate planes are as following (the numbers are given in the ;order -- real(p1), imag(p1), real(p2), imag(p2) ): ;pq-plane: 0, 0, 0, 0 pr-plane: 0, 0.5, 0, 0 ps-plane: 0.5, 0, 0, 0 ;qr: 0, 0.5, 0, 0.5 qs: 0.5, 0, 0, 0.5 rs: 0.5, 0, 0.5, 0 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1) g=pi*real(p2), d=pi*imag(p2), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g) sg=sin(g), cd=cos(d), sd=sin(d) p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd) q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd) r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q) + p3, z=r+flip(s): z=z*z+c |z|<=4 } John Ralph H. Goering johnrhg@juno.com "Let us fix our eyes on Jesus, the author and perfecter of our faith." (Heb. 12:2a NIV) ________________________________________________________________ YOU'RE PAYING TOO MUCH FOR THE INTERNET! Juno now offers FREE Internet Access! Try it today - there's no risk! For your FREE software, visit: http://dl.www.juno.com/get/tagj. 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 R Goering Subject: (fractint) Re: Animations in the Julibrot Date: 02 Aug 2000 16:41:34 -0400 Greetings, Here is a formula that simplifies the production of animations that morph the Mandelbrot set into some Julia set (or vice versa): 2DSlices { ; by John R. H. Goering ; This fractal produces 2D slices of the Julibrot set. ; p1 is the constant for some Julia set while p2 is a number ; from 0 to 1. p2=0 gives the M-set while p2=1 gives ; the J-set specified by p1. To morph from the M-set to the ; J-set, vary p2 from 0 to 1. w=pixel, a=pi*p2*0.5, c=p1*p2+w*cos(a), z=w*sin(a): z=z*z+c |z|<=4 } The basic concepts behind the development of the formula: 1) Start with a plane that slices the Julibrot through the M-set (when p2=0). 2) As p2 varies from 0 to 1, rotate and translate the plane until the plane slices the Julia set given by p1. When making animations, I have discovered that to make a smooth animation, I need to use smaller increments as p1 gets close to 1.0. For some reason, the transitions seem more abrupt as the orientation of the "slicing" plane gets closer to orientation of the Julia plane. After initially designing the formula using real numbers, I was pleasantly surprised by how simple the formula became with the use of complex numbers. John Goering View a Mandelbrot set image gallery at http://homestead.juno.com/johnrhg/files/IntroMandelbrot.html John Ralph H. Goering johnrhg@juno.com "What is lacking cannot be counted." (Ecclesiastes 1:15b NIV) So zero is not a counting number :-) ________________________________________________________________ YOU'RE PAYING TOO MUCH FOR THE INTERNET! Juno now offers FREE Internet Access! Try it today - there's no risk! For your FREE software, visit: http://dl.www.juno.com/get/tagj. 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: Mike Traynor Subject: Re: (fractint) FOTD 24-07-00 (Ring Around a Midget [7]) Date: 02 Aug 2000 23:31:05 -0400 Jim, > > FOTD -- July 24, 2000 (Rating 7) > > Fractal visionaries and enthusiasts: > > Naturally, upon finding something I've never before seen in a > fractal, my immediate impulse is to dive into it in search of > midgets. Me too. The full image itself might have been an FOTD. There is a lot of really neat stuff in this one, from these images that look like they have cables around them to other areas that have a very barnsley look to them. Mike ring22 { ; (c) Mike Traynor Aug 02, 2000 t= 0:02:21.93 ; lmtraynor@sympatico.ca ; time on PIII-600 1024x768 ; Version 2000 Patchlevel 6 reset=2000 type=formula formulafile=_m.frm formulaname=mandelbrotmix4 function=recip passes=b center-mag=+0.01684641914540264/-0.32168366776083770/8487786/1/-164.999 params=-11/-1.1/-1/-11/-1.99/0 float=y maxiter=1200 inside=bof60 logmap=62 periodicity=10 colors=0002742723873AB4BG4EK5HO<3>7Ke7Ki8Ln8Mr8Mv<8>`bycdygfy<3>smzvozsh\ v<3>iEgf7cd0`<3>hIkiMnjQpf1VZQLRnC<3>T_NUWPUSSUPU<3>iOblOdbIUTDJJ89<3>UM\ HXPJZTL<3>jdTlhVokXqnZ<3>cTb`NcYIbRD`NE_PFZSGaTHeXIhXJkYKp<2>ZNwZOyZOzYN\ y<3>XNpWNnWMk<3>UMfUMeUMd<3>NDULBSJ9PI7N<3>CCNBEN9FN8GN7HN<4>KGMMGMPFL<3\ >ZFL`FLcFLeFLgFL<3>s_ivdopbej`We_M<3>faJfaIgaH<3>gbDgbCgcBgcAgcA<5>YUEWT\ EURFTQFROG<3>LIIKHJIFJ<3>gA9m96s84y72<3>`F5UG5OI6<2>6N7<5>WQC_QDcRE<3>tS\ H<2>L0F<3>okTvvWpwV<3>VyVPzVKzV<4>DvKBvIAuF<3>4r72r51q30q1<3>4Qk5Jw9Iu<3\ >PCkTBiVAj<10>r3q } ring21 { ; (c) Mike Traynor Aug 02, 2000 t= 0:02:42.36 ; lmtraynor@sympatico.ca ; time on PIII-600 1024x768 ; Version 2000 Patchlevel 6 reset=2000 type=formula formulafile=_m.frm formulaname=mandelbrotmix4 function=recip passes=b center-mag=+0.01684645676154260/-0.32168364603497580/424389.3/1/-164.999 params=-11/-1.1/-1/-11/-1.99/0 float=y maxiter=1200 inside=bof60 logmap=62 periodicity=10 colors=0002742723873AB4BG4EK5HO<3>7Ke7Ki8Ln8Mr8Mv<8>`bycdygfy<3>smzvozsh\ v<3>iEgf7cd0`<3>hIkiMnjQpf1VZQLRnC<3>T_NUWPUSSUPU<3>iOblOdbIUTDJJ89<3>UM\ HXPJZTL<3>jdTlhVokXqnZ<3>cTb`NcYIbRD`NE_PFZSGaTHeXIhXJkYKp<2>ZNwZOyZOzYN\ y<3>XNpWNnWMk<3>UMfUMeUMd<3>NDULBSJ9PI7N<3>CCNBEN9FN8GN7HN<4>KGMMGMPFL<3\ >ZFL`FLcFLeFLgFL<3>s_ivdopbej`We_M<3>faJfaIgaH<3>gbDgbCgcBgcAgcA<5>YUEWT\ EURFTQFROG<3>LIIKHJIFJ<3>gA9m96s84y72<3>`F5UG5OI6<2>6N7<5>WQC_QDcRE<3>tS\ H<2>L0F<3>okTvvWpwV<3>VyVPzVKzV<4>DvKBvIAuF<3>4r72r51q30q1<3>4Qk5Jw9Iu<3\ >PCkTBiVAj<10>r3q } ring23 { ; (c) Mike Traynor Aug 02, 2000 t= 0:04:30.01 ; lmtraynor@sympatico.ca ; time on PIII-600 1024x768 ; Version 2000 Patchlevel 6 reset=2000 type=formula formulafile=_m.frm formulaname=mandelbrotmix4 function=recip passes=b center-mag=+0.01684642862575926/-0.32168367984283620/1.595448e+007/1/177\ .5 params=-11/-1.1/-1/-11/-1.99/0 float=y maxiter=1200 inside=bof60 logmap=62 periodicity=10 colors=0002742723873AB4BG4EK5HO<3>7Ke7Ki8Ln8Mr8Mv<8>`bycdygfy<3>smzvozsh\ v<3>iEgf7cd0`<3>hIkiMnjQpf1VZQLRnC<3>T_NUWPUSSUPU<3>iOblOdbIUTDJJ89<6>aW\ NdZPgaR<3>qnZ<3>cTb`NcYIbRD`NE_PFZSGaTHeXIhXJkYKp<2>ZNwZOyZOzYNy<3>XNpWN\ nWMk<3>UMfUMeUMd<3>NDULBSJ9PI7N<3>CCNBEN9FN8GN7HN<4>KGMMGMPFL<3>ZFL`FLcF\ LeFLgFL<3>s_ivdopbej`We_M<3>faJfaIgaH<3>gbDgbCgcBgcAgcA<5>YUEWTEURF<3>OL\ HNKILIIKHJIFJ<3>gA9m96s84y72<3>`F5UG5OI6<2>6N7<5>WQC_QDcRE<3>tSH<2>L0F<3\ >okTvvWpwV<3>VyVPzVKzV<4>DvKBvIAuF<3>4r72r51q30q1<3>4Qk5Jw9Iu<3>PCkTBiVA\ j<10>r3q } ring24 { ; (c) Mike Traynor Aug 02, 2000 t= 0:05:14.06 ; lmtraynor@sympatico.ca ; time on PIII-600 1024x768 ; Version 2000 Patchlevel 6 reset=2000 type=formula formulafile=_m.frm formulaname=mandelbrotmix4 function=recip passes=b center-mag=+0.01684642862575926/-0.32168367984283620/7.670425e+007/1/177\ .501 params=-11/-1.1/-1/-11/-1.99/0 float=y maxiter=1200 inside=2 logmap=175 periodicity=10 colors=0002742723873AB4BG4EK5HO<3>7Ke7Ki8Ln8Mr8Mv<8>`bycdygfy<3>smzvozsh\ v<3>iEgf7cd0`<3>hIkiMnjQpf1VZQLRnC<3>T_NUWPUSSUPU<3>iOblOdbIUTDJJ89<6>aW\ NdZPgaR<3>qnZ<3>cTb`NcYIbRD`NE_PFZSGaTHeXIhXJkYKp<2>ZNwZOyZOzYNy<3>XNpWN\ nWMk<3>UMfUMeUMd<3>NDULBSJ9PI7N<3>CCNBEN9FN8GN7HN<4>KGMMGMPFL<3>ZFL`FLcF\ LeFLgFL<3>s_ivdopbej`We_M<3>faJfaIgaH<3>gbDgbCgcBgcAgcA<5>YUEWTEURF<3>OL\ HNKILIIKHJIFJ<3>gA9m96s84y72<3>`F5UG5OI6<2>6N7<5>WQC_QDcRE<3>tSH<2>L0F<3\ >okTvvWpwV<3>VyVPzVKzV<4>DvKBvIAuF<3>4r72r51q30q1<3>4Qk5Jw9Iu<3>PCkTBiVA\ j<10>r3q } 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 03-08-00, (Breaking-up Midget [4]) Date: 03 Aug 2000 00:18:51 -0400 (EDT) FOTD -- August 03, 2000 (Rating 4) Fractal visionaries and enthusiasts: An extremely busy day means a hasty fractal and short discussion. Today's curious scene lies in the infinite spiral of the Z^(sqrt(2))+C Mandeloid, a short distance out from the default view. The parent fractal is a distorted bay with an even more distorted main bud. Today's scene lies in the left branch of the valley between the bay and bud. I named the picture "Breaking-up Midget" when I saw how broken the surrounding elements are. I can honestly rate the image no higher than 4, since I put almost no effort into it. The 11-minute parameter file makes a download preferable. The download may be found at: and at: The fractal weather today was partly cloudy and very muggy, with a temperature of 84F (29C) that was perfect for both fractal cats and grass trimming. The rain held off until after dark, when a heavy thunder-storm skimmed past just to the east. Luckily the rain was not enough to run into the basement. I had no time for philosophy today, but I'm accumulating a great backlog of ideas, which sooner or later will be made public. Despite the rush, I'll return in 24 hours with a new fractal and a few more words. Until then, take care, and the best has not yet arrived. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Breaking-up_Midget { ; time=0:11:06.74 -- SF5 on a p200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.09561066091537362/+0.78473810657722410\ /352024.7/1/35 params=1.414213562373/0/0/0 float=y maxiter=60000 inside=0 logmap=136 periodicity=10 colors=000WYl<3>RSoQRpPQp<21>DehCfhCgh<3>Aig<15>VEUW\ CUXAT<3>a3Q<11>iBCiBAjC9<2>lE6lE5kG4<22>jk1jl1jn1jo1\ jp1jr1jr1mm0<3>dU3aP4_K5YK5WK6TKCRKGPKKNKOLMS<2>SScU\ UfZVj<3>rTzwTzzSzwSztUoqVknXhkYdhYceZabZ`<3>URXSQWRO\ VTMU<2>ZLR<2>dWOfaNhcMjeLlgKniLomM<2>smOwmPzhPzfQzcR\ zaRx_SvYTwXU<3>vTYuSZuR_tS`tTatUb<23>XkYWlYVmX<3>RpX\ Nq_<3>ZuRavPdwNfxKiyI<3>uzAwz8vzA<6>rzIrzJqzK<3>ozOn\ zOozP<17>xzZ } frm:MandelbrotBC = { ; Z=Z^E+C Andrew Coppin e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: Re: (fractint) Branch Cuts & Julibrot Slices Date: 03 Aug 2000 01:55:40 -0400 (EDT) At 01:13 PM 8/2/00 GMT, you wrote: >But anyway... I wonder if Jim has tried animating Julibrot slices? What does >it look like to take a Mandelbrot zoom, and animate it rotating into the >Julia plane? Surely that's gotta look pretty increadible, right? Hmm... will >try... I have tried animating such rotations, but it's quite tricky. The entire M-set is not too difficult, but individual objects such as midgets are quite difficult to rotate smoothly. To start, the closer the view comes to the Julia plane, the faster it changes. Also, the Mandelbrot objects grow quite a bit larger as the Julia plane is approached, requiring several outzooms if the Julia aspect is to fit on the screen. So far I've gotten nothing but jerky results, but one of these days when I've got nothing to do, I'll have a serious go at it. 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: "Morgan L. Owens" Subject: Re: Fw: Re: (fractint) Re: 2D slices of Julibrot Date: 04 Aug 2000 11:13:08 +1200 > >Hello to all, > >Here is the mathematical derivation of the formula that I posted: > The question is whether SliceJB can provide arbitrary two-dimensional slices through the four-dimensional Julibrot. Its author, John Goering, has conjectured in the negative. I agree. Before I begin, I must say that I'll only be considering rotations through the _origin_ - that is to say, the origin [0,0,0,0] will remain fixed throughout all of these transformations. If you don't want the object to remain at the origin, you can (as in Goering's formula) move it elsewhere after you've done all your rotating. Following Goering, I label the mutually orthogonal axes of our four- dimensional Euclidean space P, Q, R, and S. But I'm not going to refer to these axes in what follows, since rotations are not so much _about_ axes as _in_ planes. This holds even in one, two and three dimensions, and is a much more sensible way of thinking about rotations if one is planning on extending any ideas about it to higher dimensions than three. For example, in two-dimensional space, there is only one plane in which rotations can occur, and in one dimension there is no room for _any_. In four-dimensional Euclidean space one can have rotations in six mutually perpendicular planes which I'll call PQ, PR, PS, QR, QS and RS. (How many ways can you choose two letters from a set of four? How many mutually perpendicular planes are there in 8-space? Hint: there are 56 mutually perpendicular volumes.) Now that I've got labels for my planes, I need to be able to specify rotations in them. Rather than try to visualise four dimensions (which can be done, I'm assured, though personally I'm still having a hard enough time with three), I'm going to resort to notation. Specifically, matrices. Goering describes the rotation of a point in the XY plane by an angle of t as: xnew=xold*cos(t) - yold*sin(t) ynew=xold*sin(t) + yold*cos(t) In matrix notation, I'll write this as [x'] = [x][cos(t) -sin(t)] [y'] [y][sin(t) cos(t)] where [x',y'] is Goering's [xnew,ynew] and [x,y] is his [xold,yold]. Let's go the whole hog and jump straight to four dimensions. To rotate a point in the PQ plane by an angle t: [p'] = [p][cos(t) -sin(t) 0 0] [q'] [q][sin(t) cos(t) 0 0] [r'] [r][ 0 0 1 0] [s'] [s][ 0 0 0 1] You'll see the effect of those ones and zeros in a second. To write out this multiplication in something Fracting can work with: pnew = pold*cos(t) - qold*sin(t) + rold*0 + sold*0 qnew = pold*sin(t) + qold*cos(t) + rold*0 + sold*0 rnew = pold* 0 + qold* 0 + rold*1 + sold*0 snew = pold* 0 + qold* 0 + rold*0 + sold*1 (You can see how the rotation matrix is reflected in this system of equations, and maybe suss out much of how matrix multiplication works from it.) Making obvious simplifications gives us pnew = pold*cos(t) - qold*sin(t) qnew = pold*sin(t) + qold*cos(t) rnew = rold snew = sold which is precisely what we expect: if we're rotating a point in the PQ plane, its R and S (or, for that matter, its T, G, or Wibble) coordinates shouldn't change. As I said, there are six orthogonal planes through any given point (and, in particular, through our origin), and each has its own matrix: PQ QR RP [ cos(t) sin(t) 0 0] [1 0 0 0] [cos(t) 0 -sin(t) 0] [-sin(t) cos(t) 0 0] [0 cos(t) sin(t) 0] [ 0 1 0 0] [ 0 0 1 0] [0 -sin(t) cos(t) 0] [sin(t) 0 cos(t) 0] [ 0 0 0 1] [0 0 0 1] [ 0 0 0 1] PS QS RS [cos(t) 0 0 -sin(t)] [1 0 0 0 ] [1 0 0 0 ] [ 0 1 0 0 ] [0 cos(t) 0 -sin(t)] [0 1 0 0 ] [ 0 0 1 0 ] [0 0 1 0 ] [0 0 cos(t) -sin(t)] [sin(t) 0 0 cos(t)] [0 sin(t) 0 cos(t)] [0 0 sin(t) cos(t)] (Which sin(t) gets the negative sign pretty much depends on whether you're left-handed or right-handed - whether you're calling the plane "PQ" or "QP".) Now, it so happens that we don't need all six. In fact, if we choose carefully, we can get by with just three! Let's say we want to rotate an object in the XZ plane, but we only have XY and YZ rotations (we'll stick to 3D for this if it helps you visualise things). What we can do is rotate the object 90 degrees in the XY plane, rotate it by the desired amount in the YZ plane, then rotate it _back_ 90 degrees in the XY plane again. The first ninety-degree rotation effectively swaps X for Y, and the second swaps it again. Doing this with (three-dimensional) transformation matrices (and I'll (a) use pi/2 radians instead of 90 degrees, 'cos radians are more natural, and (b) spell out each step in nauseating detail): [x'] = [x][cos(pi/2) -sin(pi/2) 0][1 0 0 ][cos(-pi/2) -sin(-pi/2) 0] [y'] [y][sin(pi/2) cos(pi/2) 0][0 cos(t) -sin(t)][sin(-pi/2) cos(-pi/2) 0] [z'] [z][ 0 0 1][0 sin(t) cos(t)][ 0 0 1] = [x][ 0 -1 0][1 0 0 ][ 0 1 0] [y][ 1 0 0][0 cos(t) -sin(t)][ -1 0 0] [z][ 0 0 1][0 sin(t) cos(t)][ 0 0 1] = [x*0-y*1+z*0][1 0 0 ][ 0 1 0] [x*1+y*0+z*0][0 cos(t) -sin(t)][ -1 0 0] [x*0+y*0+z*1][0 sin(t) cos(t)][ 0 0 1] = [-y][1 0 0 ][ 0 1 0] [ x][0 cos(t) -sin(t)][ -1 0 0] [ z][0 sin(t) cos(t)][ 0 0 1] (Oops, -y instead of y! Never mind: it will all come out in the wash.) = [-y*1 +x* 0 +z* 0 ][ 0 1 0] [-y*0 +x*cos(t) +z*-sin(t)][ -1 0 0] [-y*0 +x*sin(t) +z* cos(t)][ 0 0 1] = [ -y ][ 0 1 0] [x*cos(t)-z*sin(t)][ -1 0 0] [x*sin(t)+z*cos(t)][ 0 0 1] = [-y* 0 + (x*cos(t)-z*sin(t))*1 + (x*sin(t)+z*cos(t))*0] [-y*-1 + (x*cos(t)-z*sin(t))*0 + (x*sin(t)+z*cos(t))*0] [-y* 0 + (x*cos(t)-z*sin(t))*0 + (x*sin(t)+z*cos(t))*1] = [x*cos(t)-z*sin(t)] [ y ] [x*sin(t)+z*cos(t)] ...which should, (and does) equal = [x][cos(t) 0 -sin(t)] [y][ 0 1 0 ] [z][sin(t) 0 cos(t)] A rotation in the XZ plane! Huzzah! So three basis rotations are all that's needed for general four- dimensional rotations (not coincidentally one less than the number of dimensions.) Let's say they're PS, PQ and QR. Then we can do a rotation by t in PR by doing a rotation by pi/2 in PQ, a rotation by t in QR, and a rotation by -pi/2 in PQ. Achieving a rotation in SR can be done with a rotation in PS, and then one in PR (which we already know how to do), and then undoing the rotation in PS. *HOWEVER* This is all very well; but SliceJB does not provide us with an arbitrary sequence of rotations about our basis planes, because Fractint doesn't provide SliceJB with enough hooks for parameters. It provides us with the opportunity to make _four_ rotations in a _specific_ order. The first in the QS plane, the second in the QR plane, the third in the PR plane, and the fourth in the PQ plane. I'm sorry, but if all you want is a rotation in the PS or RS planes, you're out of luck. You could get an RS rotation if you could prerotate in the QS plane, do your work in the QR plane, and then undo the QS rotation, but by the time you've done the QR rotation, you can't touch the QS plane again. You can't even construct such a rotation using the remaining PR and PQ rotations (even if you could use them as many times as you like). So Goering's suspicions are justified: his SliceJB formula cannot provide every two-dimensional slice of the Julibrot. Morgan L. Owens "We need eight real parameters!" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) Re: 2D slices of Julibrot Date: 03 Aug 2000 22:07:27 -0400 (EDT) At 11:13 AM 8/4/00 +1200, Morgan Owens wrote: >The question is whether SliceJB can provide arbitrary two-dimensional >slices through the four-dimensional Julibrot. Its author, John Goering, >has conjectured in the negative. I agree. I agree also. Although I once thought the SliceJB formula could provide all possible rotations in 4-D space, I now realize that I was mistaken. I discovered this the hard way -- by trying to do the actual rotations. There are some orientations that simply cannot be reached with the formula as it is currently written. Four more parameter entries are needed if one wishes to achieve any possible rotation centered at any arbitrary point in the 4-D Julibrot object -- two entries to define the remaining rotations, two entries to define initial Z. Perhaps the developers will take the hint. Jim M. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD 04-08-00, (Something Fishy [8]) Date: 03 Aug 2000 22:35:15 -0400 (EDT) FOTD -- August 04, 2000 (Rating 8) Fractal visionaries and enthusiasts: For today's fractal image it's back to the MandelbrotMix4 and the surprises therein. The iterated formula that drew today's image results from a very small adjustment I made to the formula that drew the "Circle" and "Eutectic" FOTD images that appeared a week or so ago. Actually, it's the recently posted images by Mike Traynor that convinced me to return to the formula. The parameter adjustment involved changing real(p3), which defines a multiplication factor, from -1.999 to -1.975. This particular formula and its close variants is one of the more interesting ones I have stumbled upon in my FOTD adventures. It is so interesting because it draws fractals with inner features unlike any I have seen before -- and where there are new features, the unusual midgets can't be far behind. The trick with this formula lies in finding the midgets, which lurk hidden in places where they would be least expected. As an example, reset the logmap to 0 or 1 and back out of today's image. See if you would ever suspect that a midget such as today's would be buried where I searched. Today's rather spectacular picture rates a slightly optimistic much-above-average 8 on my 0-to-10 scale of FOTD worth. While studying the image, I suddenly got the impression that I was staring at twisted fish-tails. The name "Something Fishy" came to me within a minute. The 7-minute render time of the parameter file makes the download the better choice. That download is available from: and from: The fractal weather was variably cloudy today, with light rain at midday and a gentle thunder-shower at sunset -- all in all nothing to be concerned about. The fractal cats however dis- approved of the light midday rain, and showed their displeasure by sulking indoors all afternoon. I once again failed in my philosophical aspirations, but I'll try again tomorrow, and keep trying until I succeed. Until next time, take care, and see you in 24 hours. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Something_Fishy { ; time=0:07:02.60 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.3504712563716/-2.170429340948094/1.417\ 785e+007/1/2.499 params=-11/-1.1/-1/-11/-1.975/0 float=y maxiter=2400 inside=0 logmap=142 periodicity=9 colors=00000300000010130640A60G70L71P93TC4YF6cG7gJ9l\ MApQ6rPAuQDxTGzXJzYMz`QzcTzfXx<2>odorglulixofzrc<2>z\ zVzzTzyQzuPzpMzlLxgIscGo_DjVCfQ9aM7YL4XI3VJ6TM7SOAQQ\ CPUFOXGM_JPbLVfO_jPalSdnT`qMYsFTt7Qt0Mv0Jv0Lv0Lv0<2>\ Pw0Qw0Tv0Vv0Xv0Yv0`v0`v0Pv0`v0Yv3cv9av9`v9Yv9Tv9Px9M\ x9Ix9Dv9Av96v91u90u90s90s90y60s90oC0jF0fI0`L0XO0SQ0O\ T0JX0OT0QS1VQ6YPAaOFdLJiJOlISpGQsFPuOOuOMv9Lv7Jx6Iy4\ Gz3Fz3Dz1Cz0Az07z0Tz3gz6vz9zzC<3>zzOzzQzzTzzXzz_zzYz\ zYzzXzzXzzVzzVzzTzzTzzSzzSzzQzzQvzP<2>`zOTuQMlTFdXXX\ _fPapGdzCjz9gu7fm6d<2>V1`O0_I0YA0X40V00T30S60QA0QD0P\ I7OLFOPMMSTMV`L_gJaoJfvIizG<2>szFpzImzLjzOizQfzTczX`\ zXazYFz1<3>3zV0za0zl0zi0zf<2>9z_CzYFzVIzS<2>QzLTzJXz\ GYzD_zF`zGazIczIdzJfzLgzMgzMizOjzPlzQmzQozSpzTpzTozQ\ mzPlzMjzLjzIizGgzDfzCfz9dz7cz4az3fz0az1<5>CzSCzGAz9 } 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: "Jonathan Osuch" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 04 Aug 2000 07:48:18 -0500 Jim, > Four more parameter entries are > needed if one wishes to achieve any possible rotation centered at any > arbitrary point in the 4-D Julibrot object -- two entries to define the > remaining rotations, two entries to define initial Z. Perhaps the > developers will take the hint. I can add two more complex parameters easily. And will do so today or tomorrow. Beyond that, restructuring will be necessary. I need to be spending time on my job search, so the restructuring won't happen any time soon. 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: Jim Muth Subject: (fractint) Re: 2D slices of Julibrot Date: 04 Aug 2000 19:41:47 -0400 (EDT) At 07:48 AM 8/4/00 -0500, Jonathan Osuch wrote: >I can add two more complex parameters easily. And will do so today or >tomorrow. Great! Even as little as two more parameter entries will increase versatility an entire order of magnitude. >Beyond that, restructuring will be necessary. I need to be >spending time on my job search, so the restructuring won't happen any time >soon. No rush here. I'll be busy using the two additional parameter entries for quite a while. Jim M. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD 05-08-00, (Flashy Minibrot [6]) Date: 04 Aug 2000 21:37:07 -0400 (EDT) FOTD -- August 05, 2000 (Rating 6) Fractal visionaries and enthusiasts: Minibrots, Minibrots, Minibrots . . . will I ever get tired of Minibrots? Apparently not. Yes, I realize that they're all the same basic shape, and that I'm working myself into a rut with these Minibrots, and that some may find an endless string of midgets boring. But Minibrots are fun to find and the variety is without limit. To create today's flashy midget I changed the imag(p1) parameter of yesterday's formula from -1.1 to -1.15. The change makes a world of difference in the parent fractal and also in the shape of the midgets deep inside. I'm not going to try to describe the indescribable parent fractal; those who wish to see it may do so by resetting the logmap to 1 or 0 and outzooming from today's image until the entire fractal fits on the screen. Nor will I try to describe the flashy star-like pattern around the midget in today's image, which I have named "Flashy Minibrot" for the obvious reason. The parameter file takes over 11 minutes to render on a modest Pentium. On a state-of-the-art machine it will finish in 3 or 4 minutes. Patience may be preserved by going in a virtual manner to the Usenet group: or to the Web site of Paul Lee at: The fractal weather today was very unsettled as one thunder- storm after another billowed up nearby. Luckily none billowed up overhead, and we escaped with only a few light showers. The temperature topped out at 84F (29C), which was comfortable enough for the fractal cats, but the wet grass kept them indoors. Fractal cats don't like to get their paws wet. The big rush ended today as we delivered the final material to the organizers of the 2000 International Wushu-Kungfu Championships Festival, which is being held this weekend here in Baltimore. Next week should be slow, giving me a chance to write some of that great philosophy I've been promising for some time. I should also have the time to produce even better (if possible) fractals. For this evening however, it will be a night of rest and relaxation. Until tomorrow, take care, and a good fractal is nothing to kick about. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Flashy_Minibrot { ; time=0:11:20.44 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+8.152643939088213/+9.261915743925041/7.2\ 37436e+008/1/-155 params=-11/-1.15/-1/-11/-1.975/0 float=y maxiter=1500 inside=0 logmap=246 periodicity=9 colors=000000000500A0KF0KK0UP3UU7ZZCZcGchLcmPhrVhwZr\ zdrzhvzbvzavrVreLfUFbH3_G7HFBPEFYCJeCNnBYoAfp9rr9qs7\ zu6uv4zx0zz4ty9ssCknHkhLddPaZVZUZXObSKhPFlNApK4pH1hQ\ PU_WFibOkYZnRipLus4srGrrSprdpuporo<2>kiZifUidO<2>eX9\ dU3bR0aR0<3>fL0hK0iJ2kH3kG4lF6rE7rCAzBBzACz9Es7Fl6Cf\ 4Ba39X27R26L13G02B0060010721E23K37R3AY4Ed4Gk4Jr6Ny6P\ z7Uz7Xz7ZzAXzCUzFRzGOzJLyLJxOGvPEvSBuV9sY6rZ3pa1od0n\ f0lh0lf0if0he0ee0dd0ad1_d2Yb2Xb3Ua4Sa6Pa6OXAUSEZOGd<\ 2>CRs9Vy4Zz0fz1az7YzEUzKOzRKzZGz<2>s3xz1xz0vx0vu0ur0\ uo0s<2>f0rd0ra0pZ0pe0xY0pP0kH0eA0Z20U00O00J60FA0BA00\ <4>A00A00K40FE1BL2<2>0i40r60z70z71zA<2>dzErvFzuGzvJu\ xLpxNkyPeyRazUXzXRzYNz_HzaCzd9zeBzdCvdFrdGsdJudKvdNx\ dOydRzdSzdVzd<2>_zdZza<2>VzYUzXSzURzSRzRPzPOzONzLLzK\ KzJJzHFzFJzGLzHPzHSzJXzKZzKbzLezLizNlzOpzOszPxzRzzRz\ zSzzV } 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: "Morgan L. Owens" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 05 Aug 2000 13:53:14 +1200 At 07:48 04/08/2000 -0500, Johnathan Osuch wrote: >Jim, > > > Four more parameter entries are > > needed if one wishes to achieve any possible rotation centered at any > > arbitrary point in the 4-D Julibrot object -- two entries to define the > > remaining rotations, two entries to define initial Z. Perhaps the > > developers will take the hint. > >I can add two more complex parameters easily. And will do so today or >tomorrow. Beyond that, restructuring will be necessary. I need to be >spending time on my job search, so the restructuring won't happen any time >soon. It strikes me that it may prove worthwhile in the longer term (it would no doubt need significant redesign, though) to allow for an arbitrary number of parameters (p1, p2, p3, ...), rather than hardcoded restrictions. Morgan L. Owens "But if you need 50+ parameters, you're probably trying to do too much at once." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 05 Aug 2000 08:02:15 -0500 Morgan, > It strikes me that it may prove worthwhile in the longer term (it would no > doubt need significant redesign, though) to allow for an arbitrary number > of parameters (p1, p2, p3, ...), rather than hardcoded restrictions. The major problems with that are how do you display them on the screen and how do you store/retrieve them from GIF files. Realizing that the GIF file format is eventually going away (the ability to read them will stay for a while), there may be a way to store an arbitrary number of variables with the png file format. That still leaves the problem with the input screens. 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: John R Goering Subject: (fractint) Re: 2D slices of Julibrot Date: 05 Aug 2000 11:35:37 -0400 Thank you, Morgan Owens, for the explanation of rotations in 4D. I have just a B.S. degree in Mathematics and never formally studied 4D, so I really appreciate this information. When Fractint will allow us to write a formula that can do 6 rotations of a plane in 4D and then move the origin of that plane to any point in 4-space, what would be the best sequence of 6 rotations? Or is there no *best* sequence? For example, in PQRS-space, would it be better for the first two rotations to be independent of each other (e.g., a rotation in QS and one in PR), or would it be better for the second rotation to be dependent on the first rotation (e.g., a rotation in QS and then one in QR)? Or doesn't it matter? With lots of questions, John Goering View a Mandelbrot set image gallery at http://homestead.juno.com/johnrhg/files/IntroMandelbrot.html John Ralph H. Goering johnrhg@juno.com "Now set your heart and your soul to seek the LORD your God." (I Chron. 22:19a) ________________________________________________________________ YOU'RE PAYING TOO MUCH FOR THE INTERNET! Juno now offers FREE Internet Access! Try it today - there's no risk! For your FREE software, visit: http://dl.www.juno.com/get/tagj. 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: "Damien M. Jones" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 05 Aug 2000 13:43:13 -0400 John, - For example, in PQRS-space, would it be better for the first two - rotations to be independent of each other (e.g., a rotation in QS - and one in PR), or would it be better for the second rotation to - be dependent on the first rotation (e.g., a rotation in QS and - then one in QR)? Or doesn't it matter? I too would like to know. I've recently been exploring my own 4D rotation formulas, and it is hard to predict what the six rotations I've got are actually doing. One advantage to doing the first two rotations independently is that, if your 4D object is the Julibrot, you can go from Mandelbrot to Julia with just the first two rotations. That's easy enough to figure. I'm particularly interested in generalized 4D rotations because the same technique can be used to explore the Julibrot, quaternion M and J, hypercomplex M and J, Julia2 space, etc. It's just a generally useful tool in the fractal formula toolbox. More parameters in formulas would be good, always. As for interface--might I suggest displaying the formula text on a separate screen (keeping it scrollable)? That would leave lots of room for additional parameters while retaining the ability to view the formula text, which often has hints as to how to use the formula. Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ Please do not post my e-mail address on a web site or in a newsgroup. Thank you. 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: comdotatdotcom@csi.com Subject: RE: Re: (fractint) Re: 2D slices of Julibrot Date: 05 Aug 2000 22:37 0000 Hi Folks, >The major problems with that are how do you display them on the screen >and how do you store/retrieve them from GIF files. Realizing that the GIF Not to mention that the evolver would need a bit of a rethink to cope with arbitary numbers of parameters too.... Surely enough parms to define plane and rotation in a 4D volume would do for now! Cheers, Robin. 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) Patch 13 Date: 05 Aug 2000 19:24:14 -0500 Patch 13 is on the ftp site. The executable is there as fradev20.0.13.zip. This patch adds parameters p4 and p5 to the formula parser and now checks all the parameters when the symmetry options XAXIS_NOREAL and XAXIS_NOIMAG are used. I purposely did not add the two new parameters to the evolver. Maybe someday. 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: Jim Muth Subject: (fractint) FOTD 06-08-00, (A Flawed Fractal [2]) Date: 05 Aug 2000 22:26:54 -0400 (EDT) FOTD -- August 06, 2000 (Rating 2) Fractal visionaries and enthusiasts: Today's modest effort rates only a humble 2 on my scale of worth. I had originally rated it a 5, but then I realized that a better image lies closer in toward the midget. This realization caused me to consider today's image flawed, and as a result I dropped its rating to 2 and named it "A Flawed Fractal". But it is flawed only in comparison to what it might have been, and in fact might turn out to be in a soon-to-appear FOTD. The formula is once again a combination of various portions of Z^(-1.1) and Z^(-11) plus 1/C. Minor variations of this formula produce images of the most interesting kind, with midgets of an even more interesting nature lurking within. The parameter file takes an exasperatingly long time to render even on a Pentium machine. But relief is as near as the internet, where the GIF file has been posted to Usenet at: and to the Web at: The fractal weather today was perfect -- the first day in several weeks that I heard no thunder and saw no rain. The deep blue sky, puffy clouds, dry atmosphere, and temperature of 83F (28C) brought out both the neighborhood lawn mowers and the fractal cats. The great conditions also brought out the philosophy in me. Having just completed the program magazine for the 2000 Kung-Fu Competition, I pondered the nature of the martial-art discipline known as Kung-Fu. After working closely with the organizers for several weeks, I have come to realize that the art of Kung-Fu involves as much spiritual discipline as physical prowess. In fact, when studying the art, one learns how to direct and focus a spiritual energy known as Qi, or sometimes Chi. The more skeptical among us tell that such energy does not exist, that those who claim to be using Qi energy are actually skillfully using well-known natural laws of physics. When I mentioned this to one of the Kung-Fu masters, he merely laughed. "Who knows more about Qi energy?" he replied. "Those who have worked with it all their lives or those who do not yet know that it exists?" Then he gave me a brief demonstration of the energy in action. The tingly heat I felt could have been the power of suggestion, or a natural physiological effect, or it could have been Qi energy. Since the Kung-Fu master knew more about the topic than I, and he claimed that the heat was caused by an actual spiritual energy, I must take the word of the expert. I find it a bit incredible that Kung-Fu students would devote so much effort to working with something that does not exist, and after hundreds of years have still not discovered that it does not exist. As for me, I'm undecided whether it exists, but I have no doubt that 'Qi' is a good scrabble word. And of course, I'll be here again in 24 hours with another fractal, this next one guaranteed to rate higher than today's. And I'll also have some more words of wisdom. Until then, take care, and fractals are forever. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Flawed_Fractal { ; time=0:25:31.92 -- SF5 0n a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.01733612521571942/+1.594853495298927/1.\ 182371e+010/1/125.003 params=-11/-1.1/-1/-11/-1.975/0 float=y maxiter=6000 inside=0 logmap=149 periodicity=9 colors=000R62T62<3>gQQjVWn_a<2>xns<3>kskhtjeuh<2>Xxb\ UyaTwc<8>TnoTmqTlr<2>TivThwUet<4>UWjVUgVSe<3>VKY<3>c\ YMe`JhcG<3>pp5<7>md_mccmag<3>lXv<3>jpmjtkkrl<7>lfple\ qmcq<2>m_smZsk_r<3>ebqdcqbdqaeq`eq<6>XMrXJrWGr<3>V5r\ k2c<8>eHOeJMdLK<3>bRE<3>HZZB`c6bh<3>FlkHokJqlLsl<3>R\ PXTITUAPV3M<9>eaTfeUghV<2>jsXkvXjuY<5>dt_ct`bs`<3>_s\ a<2>huZkuYlna<3>nRqnLtoLt<3>qMtqNtrNtrNt<3>oQqVjXnRp\ <17>_eaZf`Zf`<3>VjXyNB<3>`fTHxq<13>RncRnbSma<3>VjYGb\ N } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) Re: Patch 13 Date: 05 Aug 2000 22:30:40 -0400 (EDT) At 07:24 PM 8/5/00 -0500, you wrote: >Patch 13 is on the ftp site. The executable is there as fradev20.0.13.zip. I'm eager to get my hands on the latest patch, but I can't find the address of the ftp site. What is the full address? 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: "Damien M. Jones" Subject: Re: (fractint) Re: Patch 13 Date: 05 Aug 2000 22:46:38 -0400 Jim, - I'm eager to get my hands on the latest patch, but I can't find the - address of the ftp site. What is the full address? Have a look here: http://www.fractint.org/ftp/ Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ Please do not post my e-mail address on a web site or in a newsgroup. Thank you. 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: Bob Margolis Subject: Re: (fractint) Re: Patch 13 Date: 05 Aug 2000 21:42:23 -0500 Jim Muth wrote: > > > I'm eager to get my hands on the latest patch, but I can't find the > address of the ftp site. What is the full address? > http://www.fractint.org/ftp/ Cheers, Bob Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 06 Aug 2000 15:38:04 +1200 At 08:02 05/08/2000 -0500, you wrote: >Morgan, > > > It strikes me that it may prove worthwhile in the longer term (it would no > > doubt need significant redesign, though) to allow for an arbitrary number > > of parameters (p1, p2, p3, ...), rather than hardcoded restrictions. > >The major problems with that are how do you display them on the screen >and how do you store/retrieve them from GIF files. Realizing that the GIF >file format is eventually going away (the ability to read them will stay for >a while), there may be a way to store an arbitrary number of variables with >the png file format. That still leaves the problem with the input screens. Having been writing medical software lately involving forms with a couple of hundred fields, I find myself resonating with this question! The problem I take it is that as the number of parameters bloats, so too does the number of lines required to display them in the screen. Four thoughts occur to me: Already, parameters are only listed in the screen if they actually appear in the code (if you only mention p1 and p3, then only p1 and p3 get listed). It's only sane to continue with this: if someone mentions (say) p12, p13, p14, p23, p24 and p34 (for representing rotations in 4-space) in their formula, then there is no point in the screen even trying to list thirty-four parameters. As I suggested, someone who asks for fifty parameters is asking for trouble, but some sort of scrolling may be the most graceful way of accommodating such stunts, rather than an ad hoc complaint from the parser (if it's the UI's problem, the parser shouldn't have to worry about it). At present, the parameters are listed like this: Real portion of p1 space for 20 digits. Imaginary portion of p1 0 Real portion of p2 0 Imaginary portion of p2 0 Real portion of p3 0 Imaginary portion of p3 0 But summat like: Real portion Imaginary portion p1 Space for 20 digits. Space for 20 digits. p2 0 0 p3 0 0 is only two characters wider, and almost halves the height. Tabbing between fields would zigzag from left to right down the list. It has the bonus advantage of more closely relating the real and imaginary parts of a complex number (and also groups the real parts and imaginary parts together for situations where only real parts are being used). The final thought is longer term: the text-mode UI will almost surely give way to a graphics-mode interface eventually, making much of this discussion moot by giving easy access to a more sophisticated interface widgetry (though I myself would insist on retaining the ability to simply hit to bring up the parameter dialogue, and typing numerical values for parameters). Morgan L. Owens "There's a standard medical code for injuries sustained while a passenger in an unidentified flying object." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 06 Aug 2000 23:38:10 +1200 At 11:35 05/08/2000 -0400, John Goering wrote: >When Fractint will allow us to write a formula that can do 6 rotations of >a plane in 4D and then move the origin of that plane to any point in >4-space, what would be the best sequence of 6 rotations? Or is there no >*best* sequence? > >For example, in PQRS-space, would it be better for the first two >rotations to be independent of each other (e.g., a rotation in QS and one >in PR), or would it be better for the second rotation to be dependent on >the first rotation (e.g., a rotation in QS and then one in QR)? Or >doesn't it matter? There are at least two ways in which a given sequence of rotations might be considered the *best* - intuitive ease of use and elegance of coding. Both approaches suggested by John would appear to be the best by one or the other of these ways. The most intuitive (for some definition of "intuitive") is probably to build up rotations in higher dimensions by successively "tuning" in each dimension in turn: First do a rotation in 2 dimensions: PQ; then the rest of the rotations in 3 dimensions: PR, QR; then the rest of the rotations in 4 dimensions: PS, QS, RS; then (if you're feeling adventurous) you can follow with rotations in PT, QT, RT, and ST.... While this looks like the most straightforward approach for use, it can lead to some ungainly and lopsided-looking coding: xnew=((xold*cos(t1)+yold*sin(t1))*cos(t2)+zold*sin(t2))*cos(t4)-wold*sin(t4) ynew=((yold*cos(t1)-xold*sin(t1))*cos(t3)+(zold*cos(t2)-(xold*cos(t1)+yold*sin(t1))*sin(t2))*sin(t3))*cos(t5)-(wold*cos(t4)+((xold*cos(t1)+yold*sin(t1))*cos(t2)+zold*sin(t2))*sin(t4))*sin(t5) znew=((zold*cos(t2)-(xold*cos(t1)+yold*sin(t1))*sin(t2))*cos(t3)-(yold*cos(t1)-xold*sin(t1))*sin(t3))*cos(t6)-((wold*cos(t4)+((xold*cos(t1)+yold*sin(t1))*cos(t2)+zold*sin(t2))*sin(t4))*cos(t5)+((yold*cos(t1)-xold*sin(t1))*cos(t3)+(zold*cos(t2)-(xold*cos(t1)+yold*sin(t1))*sin(t2))*sin(t3))*sin(t5))*sin(t6) wnew=((wold*cos(t4)+((xold*cos(t1)+yold*sin(t1))*cos(t2)+zold*sin(t2))*sin(t4))*cos(t5)+((yold*cos(t1)-xold*sin(t1))*cos(t3)+(zold*cos(t2)-(xold*cos(t1)+yold*sin(t1))*sin(t2))*sin(t3))*sin(t5))*cos(t6)+((zold*cos(t2)-(xold*cos(t1)+yold*sin(t1))*sin(t2))*cos(t3)-(yold*cos(t1)-xold*sin(t1))*sin(t3))*sin(t6) though other representations are cleaner-looking: nx=x*cos(t1)+y*sin(t1), ny=y*cos(t1)-x*sin(t1), x=nx, y=ny nx=x*cos(t2)+z*sin(t2), nz=z*cos(t2)-x*sin(t2), x=nx, z=nz ny=y*cos(t3)+z*sin(t3), nz=z*cos(t3)-y*sin(t3), y=ny, z=nz nx=x*cos(t4)-w*sin(t4), nw=w*cos(t4)+x*sin(t4), x=nx, w=nw ny=y*cos(t5)-w*sin(t5), nw=w*cos(t5)+y*sin(t5), y=ny, w=nw nz=z*cos(t6)-w*sin(t6), nw=w*cos(t6)+z*sin(t6), z=nz, w=nw or x1=x0*cos(t1)+y0*sin(t1), y1=y0*cos(t1)-x0*sin(t1) x2=x1*cos(t2)+z0*sin(t2), z1=z0*cos(t2)-x1*sin(t2) y2=y1*cos(t3)+z1*sin(t3), z2=z1*cos(t3)-y1*sin(t3) x3=x2*cos(t4)-w0*sin(t4), w1=w0*cos(t4)+x2*sin(t4) y3=y2*cos(t5)-w1*sin(t5), w2=w1*cos(t5)+y2*sin(t5) z3=z2*cos(t6)-w2*sin(t6), w3=w2*cos(t6)+z2*sin(t6) The other alternative suggested is to concentrate on independent pairs of rotations. A rotation in the PQ plane affects neither the R nor S coordinates of a point, and a rotation in the RS plane leaves the P and Q coordinates similarly untouched. So rotating by an angle t1 in the PQ plane then rotating by an angle of t2 in the RS plane has the same net effect as a rotation by t2 in the RS plane followed by a rotation by t1 in the PQ plane (assuming that the two rotations are consecutive). There are four pairs of mutually independent planes: PQ/RS, PR/QS and PS/QR (which reflects the fact that two planes are independent if they have no axes in common). The code that's produced by this sequence of rotations is more symmetric (at least in a long enough line width): xnew=((xold*cos(t1)+yold*sin(t1))*cos(t3)-(zold*cos(t2)-wold*sin(t2))*sin(t3))*cos(t5)-((wold*cos(t2)+zold*sin(t2))*cos(t4)+(yold*cos(t1)-xold*sin(t1))*sin(t4))*sin(t5) ynew=((yold*cos(t1)-xold*sin(t1))*cos(t4)-(wold*cos(t2)+zold*sin(t2))*sin(t4))*cos(t6)+((zold*cos(t2)-wold*sin(t2))*cos(t3)+(xold*cos(t1)+yold*sin(t1))*sin(t3))*sin(t6) znew=((zold*cos(t2)-wold*sin(t2))*cos(t3)+(xold*cos(t1)+yold*sin(t1))*sin(t3))*cos(t6)-((yold*cos(t1)-xold*sin(t1))*cos(t4)-(wold*cos(t2)+zold*sin(t2))*sin(t4))*sin(t6) wnew=((wold*cos(t2)+zold*sin(t2))*cos(t4)+(yold*cos(t1)-xold*sin(t1))*sin(t4))*cos(t5)+((xold*cos(t1)+yold*sin(t1))*cos(t3)-(zold*cos(t2)-wold*sin(t2))*sin(t3))*sin(t5) but in reality there is no significant saving of computation, as is shown by representations analogous to the other two above: nx=x*cos(t1)+y*sin(t1), ny=y*cos(t1)-x*sin(t1), x=nx, y=ny nz=z*cos(t2)-w*sin(t2), nw=w*cos(t2)+z*sin(t2), z=nz, w=nw nx=x*cos(t3)-z*sin(t3), nz=z*cos(t3)+x*sin(t3), x=nx, z=nz ny=y*cos(t4)-w*sin(t4), nw=w*cos(t4)+y*sin(t4), y=ny, w=nw nx=x*cos(t5)-w*sin(t5), nw=w*cos(t5)+x*sin(t5), x=nx, w=nw ny=y*cos(t6)+z*sin(t6), nz=z*cos(t6)-y*sin(t6), y=ny, z=nz and x1=x0*cos(t1)+y0*sin(t1), y1=y0*cos(t1)-x0*sin(t1) z1=z0*cos(t2)-w0*sin(t2), w1=w0*cos(t2)+z0*sin(t2) x2=x1*cos(t3)-z1*sin(t3), z2=z1*cos(t3)+x1*sin(t3) y2=y1*cos(t4)-w1*sin(t4), w2=w1*cos(t4)+y1*sin(t4) x3=x2*cos(t5)-w2*sin(t5), w3=w2*cos(t5)+x2*sin(t5) y3=y2*cos(t6)+z2*sin(t6), z3=z2*cos(t6)-y2*sin(t6) Again, the rotations taken in order are t1..t6 for the sequence of rotations PQ RS PR QS PS QR. Whether this is easier for a user to work with, however, is questionable (at least, I find both equally obscure), and requires experimentation. In total, there are thirty (6!/4!) distinct orders in which the rotations can be made (up to a relabelling of the axes): PQ PR PS QR QS RS PQ PR PS QR RS QS PQ PR PS QS QR RS PQ PR PS QS RS QR PQ PR PS RS QR QS PQ PR PS RS QS QR PQ PR QR PS QS RS PQ PR QR PS RS QS PQ PR QR QS PS RS PQ PR QR QS RS PS PQ PR QR RS PS QS PQ PR QR RS QS PS PQ PR QS PS QR RS PQ PR QS PS RS QR PQ PR QS QR PS RS PQ PR QS QR RS PS PQ PR QS RS PS QR PQ PR QS RS QR PS PQ PR RS PS QR QS PQ PR RS PS QS QR PQ PR RS QR PS QS PQ PR RS QR QS PS PQ PR RS QS PS QR PQ PR RS QS QR PS PQ RS PR PS QR QS PQ RS PR PS QS QR PQ RS PR QR PS QS PQ RS PR QR QS PS PQ RS PR QS PS QR PQ RS PR QS QR PS This assumes that there is nothing to distinguish one axis from another, though, and most have nothing to commend them. If different axes are interpreted differently (as they are in the formula) then there can be as many as 720 different orders. However you specify a plane in 4-space, you're looking at at least ten real parameters - six rotations and a point being one example. Other ways of defining a plane, such as three points or a point and two vectors, might be considered, but both have twelve parameters and without some preprocessing one can end up with distortions (if, for example you make the unwarranted assumption that the two vectors are at right angles when in fact they need not be). They may not be so useful, but if its easy to find the coordinates of three noncolinear points in the plane you're interested in, then a three-point specification of the plane may well be the way to go. Morgan L. Owens "Me? I just stick to the combinatorics..." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 06 Aug 2000 17:06:59 -0500 Morgan, > Already, parameters are only listed in the screen if they actually > appear in the code (if you only mention p1 and p3, then only p1 and p3 get > listed). It's only sane to continue with this: if someone mentions (say) > p12, p13, p14, p23, p24 and p34 (for representing rotations in 4-space) in > their formula, then there is no point in the screen even trying to list > thirty-four parameters. Even with only p1 through p3 there were cases that didn't work. I ended up reworking the logic, so it should always work now. At least all my test cases worked. Just don't look closely at the screen. 8-)) > At present, the parameters are listed like this: > Real portion of p1 space for 20 digits. ... > But summat like: > Real portion Imaginary portion > p1 Space for 20 digits. Space for 20 digits. > p2 0 0 ... > is only two characters wider, and almost halves the height. Tabbing between > fields would zigzag from left to right down the list. It has the bonus > advantage of more closely relating the real and imaginary parts of a > complex number (and also groups the real parts and imaginary parts together > for situations where only real parts are being used). Yes, that would work very well. It involves changing a routine used to display all the menus in Fractint. The changes will have to be done very carefully. 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: "Damien M. Jones" Subject: (fractint) Fractal-Art 2000 Contest Date: 06 Aug 2000 23:10:55 -0400 Greetings folks, It is my pleasure to announce that the Fractal-Art 2000 Contest web site is officially open. It is available for your viewing pleasure here: http://www.contest2k.com/ This contains the official, final rules. Next weekend I'll open up the submissions area, but I wanted to get the rules posted so people can look at them. I expect most people who've been interested in the contest have been preparing entries in advance, anyway. :) Some have suggested that including the contest URL in your signature will help get the site more exposure, especially amongst those who are not fractal enthusiasts. Everyone is of course welcome to do this. Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ Please do not post my e-mail address on a web site or in a newsgroup. Thank you. 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 07-08-00, (Storm Clouds [5]) Date: 07 Aug 2000 00:46:37 -0400 (EDT) FOTD -- August 07, 2000 (Rating 5) Fractal visionaries and enthusiasts: The fractal weather today was rainy with occasional thunder. In honor of the damp occasion I produced a fractal that comes complete with dark billowing storm clouds and streaks of lightning. It should come as no surprise that in the midst of the turmoil lies the everpresent midget. The iterated formula that created today's stormy fractal is a close relative of the "Eutectic" formula of a week or so ago, though today I changed the second exponent of Z from -11 to -15 and changed the multiplication factor to -0.95. Though today's image was calculated by the MandelbrotMix4 formula, there may soon be a MandelbrotMix3 formula, which will take advantage of the additional parameter entries in the latest patch of Fractint. Yes, I realize that the sensible name for the next formula would be MandelbrotMix5, but I have never been one to do sensible things. With a running time of only a bit over one minute, the parameter file will recreate the image as fast as the GIF file can be downloaded from: or from: The fractal weather today was cloudy with moderate rain all afternoon, accompanied by thunder at times. The temperature of 75F (24C)was fair enough, but fractal cats don't like getting their paws wet, so they stayed indoors all day. The philosophy is coming, though it's not yet finished. Tomorrow may be the big day, so check then to see. Until next time, take care, and just because I say something doesn't make it true. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Storm_Clouds { ; time=0:01:37.60 -- SF5 on a P200 ; Version 2000 Patchlevel 13 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.03468569020349364/+2.160487799666177/1\ .060033e+008/1/-24.999 params=-11/-1.1/-1/-15/-1.95/0 float=y maxiter=300 inside=0 logmap=22 periodicity=10 colors=000007007<3>00D00E00F<2>40J60K72M83NA4O74O67N\ 68N6BN4DN4EM4HM4IM3JM3MM3NK2OK2RK2SK2UKFNJ<2>o7JrBI\ <3>wNIyQIzUIzXHzZHzbHzeHzgH<2>zqHzrFzsEzsDzuBzuAzv8z\ v8zw7yw6wy4vy3uz2sz2rz0<3>mz0kz0gz7cyI_vSXucSrnOoyKn\ zHrvDuj8wZ4zN2zB4z87z78z6By3Ey2Fw0Iw0Kv0Mv0Ns0Or0Qq0\ Rn2Um3Vj4Xi6Yj8ZkA_lBbmDcnFeoHfpIiqKgrJBscFtaIu_KvZN\ wYQxVSyUXzSZzRazOczNfzMIzu<3>Yz_azVezQszBrzDrzDqzEqz\ EozFozFnzHnzHmzHmzIkzI<3>izK0ze<2>0za<3>DzXHzVJzVMzU\ QzSSzRVzQYzOazNczMfzK2zz7zwDzrHzmMzgRzcVzZ_zUezOez_\ <3>fzYfzXfzXfzVfzVgzUgzUgzS<3>gzQgzQizO<3>izMizMizKB\ zXEzVFzVHzUIzUKzSMzSNzSOzRRzRSzQUzQVzOYzOZzO<2>czMez\ MfzKgzK0z00z00z02z03z06z07z0Az2Bz3Ez3Fz4Iz6Jz7Kz7Nz8\ OzARzBSzDVzDXzEZzF_zHbzHczIfzJgzKvzeuzcuzbszbszarz_\ <2>qzYqzYozXozVozVnzUnzSmzSmzR } 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: "Morgan L. Owens" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 07 Aug 2000 23:36:03 +1200 At 17:06 06/08/2000 -0500, Jonathan Osuch wrote: >Morgan, > > ... summat like: > > Real portion Imaginary portion > > p1 Space for 20 digits. Space for 20 digits. > > p2 0 0 >... > > is only two characters wider, and almost halves the height. > >Yes, that would work very well. It involves changing a routine used to >display all the menus in Fractint. The changes will have to be done very >carefully. Heh, I suspected as much :). How close to the horizon is a graphic-mode windowing interface? Is it be worth the effort to do something fiddly if it will be trashed soon enough anyway? After all, the suggested layout would only stave off the problem of large numbers of parameters for a while, not solve it - and something that would (like a scrolling list) would be even harder to code. Morgan L. Owens "No, it's inevitable. No matter how many knobs are added and no matter what they all do, some bright spark will think of something that needs another one." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 07 Aug 2000 07:47:48 -0500 Morgan, > How close to the horizon is a graphic-mode > windowing interface? Is it worth the effort to do something fiddly if it > will be trashed soon enough anyway? I wouldn't expect to see a graphic-mode windowing interface for a while (6-12 months). I am working on integrating the Allegro graphics package into the Xfractint source. This work is almost complete as far as the graphics modes is concerned. Once that is done, we need to port the code over to djgpp and/or a windows compatible compiler. The problem with making changes to the old source is that it takes time away from the new source. I do need a break occasionally, which is why I work on tracking down bugs that are reported. 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: "Fernando Bresslau" Subject: Re: (fractint) FOTD 07-08-00, (Storm Clouds [5]) Date: 07 Aug 2000 10:18:07 -0300 Hey, Jim, I´m eager to get my hand ond you mandelbrotmix3!! Fernando Bresslau http://www.fractal.art.br __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.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: "Fernando Bresslau" Subject: Re: (fractint) FOTD 07-08-00, (Storm Clouds [5]) Date: 07 Aug 2000 10:34:49 -0300 ----- Original Message ----- Sent: Monday, August 07, 2000 10:18 AM > Hey, Jim, I´m eager to get my hand ond you mandelbrotmix3!! > Fernando Bresslau > http://www.fractal.art.br > > > > __________________________________________________ > Do You Yahoo!? > Talk to your friends online with Yahoo! Messenger. > http://im.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" __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.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: "Fernando Bresslau" Subject: Re: (fractint) FOTD 07-08-00, (Storm Clouds [5]) Date: 07 Aug 2000 10:36:16 -0300 Lots of typing mistakes, sorry. "my handS", "on" and "your". yes, this was a useless email, but traffic is low anyway... Fernando ----- Original Message ----- > Hey, Jim, I´m eager to get my hand ond you mandelbrotmix3!! > Fernando Bresslau > http://www.fractal.art.br __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.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: "Fernando Bresslau" Subject: Re: (fractint) FOTD 07-08-00, (Storm Clouds [5]) Date: 07 Aug 2000 10:36:27 -0300 Lots of typing mistakes, sorry. "my handS", "on" and "your". yes, this was a useless email, but traffic is low anyway... Fernando ----- Original Message ----- > Hey, Jim, I´m eager to get my hand ond you mandelbrotmix3!! > Fernando Bresslau > http://www.fractal.art.br __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.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: "Ivan Muccinelli" Subject: (fractint) fractal 2D/3D animation Date: 07 Aug 2000 21:59:07 +0200 Hi everybody. I wrote a program (another one!) to generate 2d/3d animations (fli/flc) with Fractint, with color map transition, rotation, morphing, output to Povray 3.0, user interface, and other. Obviously freeware. If someone is interested in looking at it (and eventually tell me what he thinks about it), I've put a beta version at: http://web.tiscalinet.it/freego_rifero. Sorry if you're not interested. Bye 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 08-08-00, (Hopi [6]) Date: 08 Aug 2000 01:04:51 -0400 (EDT) FOTD -- August 08, 2000 (Rating 6) Fractal visionaries and enthusiasts: The FOTD is a little late tonight due to a 2-hour power failure caused by a crackling electrical storm. They said there were over 3000 lightning strikes in the area this evening. At least 1000 must have been within a half kilometer of Fractal Central. Luckily, I had found my fractal before the power went off. The formula 10.45(Z^(-1.2))+0.95(Z^(-11))+(1/C) was iterated, and the bailout was raised to 10,100 to produce the fractal. The parent fractal is another variation of the parent fractal of the "Circle" image of a week or so ago. This image was once again created with the MandelbrotMix 4 formula. I'm working on MandelbrotMix3, which will begin producing FOTD fractals as soon as I get it right. I named the image "Hopi" because of the hoop around the tiny midget at the center, and also because the Hopis of the southwest USA supposedly have the ability to create rain by performing their rain dance. After seeing the deluge of rain this evening, I'm convinced that some Hopis must have been doing a rain dance in the vicinity. With a render time of 5 minutes, the parameter file is a bit slow. Relief may be found by downloading the fully rendered GIF image from the Usenet binary group: or from Paul Lee's web site at: The fractal weather today was very warm and muggy, with a light thunder-shower in the afternoon and a real whopper in the evening. The temperature of 93F (34C) was a bit too warm for the fractal cats, who remained inside, within a short dash of their hiding places when the storms came up. Sorry, philosophy-starved fans, the philosophy went nowhere again today. But keep checking -- one of these days you'll be pleasantly surprised. Until tomorrow, when philosophy or not, there will be a fractal, take care, and never give up hope. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Hopi { ; time=0:05:00.55 -- SF5 0n a p200 ; Version 2000 Patchlevel 13 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.23484599515930000/+1.31138272396386500\ /1.479015e+011/1/87.497/0.002 params=-11/-1.2/-1/-11\ /-1.95/10000 float=y maxiter=1200 bailout=25 inside=0 logmap=102 mathtolerance=/1 periodicity=10 colors=000W0_<3>Y1bZ4cZ7d_6h_4k`2w`1zN0ZH0ZA09402000\ 0100700B00H00L00R00Y00a00h00l00s00y0<2>0z09z0Gy0Ns0V\ k0ac0iY0qQ0yK0<2>kL1<3>TLIOLNKLRGLWBL`7Ld4Lh6Qd7Ta9Y\ ZA`YBdVDhRElQGoNHtKIxHKzGLzDNzANz9RzEVzKYzO`yVdv`hsd\ koknlqqividy<3>HTzAQz4Nz2Vz1`v<3>0yR0zK0zK0zI<2>0zG1\ zG2zE2zE4yD6yD6xBYh07xB9vAAv9Av9Bt7Dt7Es6Es6Gs4Hq2Iq\ 2Io1Ko1Ln0Ln0Nn0Ol0Ql0Qk0Rk0Tk0Vi0Vi0Wh0Yh0c`zaaz<6>\ aazaazaaz<3>aayaaxaaxaavaavaataatacsacsacqacoaco`cn`\ cn`cl`cl`ck`ck`ci`ci`dh`ff`hf`id`kd`lc`nc`oa`qa`s``t\ ``vZ`xY`yY`zW`zW`zVZzVZzTZzTZzRZzRZzQZzOZzOZzNZzNZzL\ ZzLZzKZzKZzI<2>ZzGZzGZzEZzEZzDZzDZzB<2>YzAYz9Yz7Yz7Y\ z6Yz6Yz4Yz4Yz2<3>Yz0Yz0Yz0<3>Yz0Yz0Yz0<2>Yz0oztnzsnz\ qnzonzolznlzllzklzknz0iz0dz0`z4Wz9RzDOzH<2>BzV7zZ4zc\ 0zh<3>0zz0zy1zx } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) Re: FOTD 07-08-00 Date: 08 Aug 2000 01:08:20 -0400 (EDT) At 10:18 AM 8/7/00 -0300, Fernando Bresslau wrote: >Hey, Jim, I=B4m eager to get my hand ond you mandelbrotmix3!! >Fernando Bresslau I'm working on it, but it will be a few days before the new formula=20 is ready. I haven't even decided yet what I want it to do! Jim M. =20 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: "Ivan Muccinelli" Subject: (fractint) fractal 2D/3D animation Date: 08 Aug 2000 19:59:08 +0200 Hi everybody. If someone of you downloaded my program for 2d/3d fractal animation, well, I apologize for the mistake... I forgot to include the tutorial file in the zip archive. Anyway, you can download it at the web site now (together with a complete beta2). It's just 10 Kb zipped, not a great traffic. Thanks to Mark Christenson who told me. Bye. Ivan 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 09-08-00, (A Fractal for the Ages [7]) Date: 08 Aug 2000 22:10:39 -0400 (EDT) FOTD -- August 09, 2000 (Rating 7) Fractal visionaries and enthusiasts: The formula 10Z^(-1.1)+0.95Z^(-11)+(1/C) was iterated to produce today's image. Although the parameters appear quite a bit different from those of the past several days, the changes amount to no more than a simplification of the old parameters. The images the formulas draw remain unchanged. I named today's fractal "A Fractal for the Ages", not because it is so great that it will be remembered through the ages, but because I liked the sound of the phrase. The image is rather striking, with a kind of ceremonial effect that is hard to describe. In my current opinion it rates a 7; tomorrow or next month I may feel entirely different about it. The 5-minute draw time stretches the limits of reasonability. To make things more reasonable I have posted the GIF image to the Usenet group: and to the Web at: The fractal weather today was sunny with no rain for a change. But the fractal cats decided that the temperature of 95F (35C) was a bit too warm, and passed the day in the coolness of the air-conditioned Fractal Central. The philosophical ponderings, which have been so conspicuously absent lately, are once again absent today. But anything worth having is worth waiting for, so keep the faith and eventually the enlightenment will come. For now, I'm going to call it a night, close down Fractal Central, enlighten myself into the chair in front of the TV, and see how junky a show I can find. Until tomorrow, take care. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ AFractalForTheAges { ; time=0:05:13.45 -- SF5 on a P200 ; Version 2000 Patchlevel 13 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.7081770276621348/-18.7005721594379/1.8\ 84167e+008/1/92.499 params=10/-1.1/0.95/-11/0/400 float=y maxiter=1200 inside=0 logmap=98 periodicity=9 colors=000I8`<2>Q2U<2>446UK7XP7mX8ra8zcEjYJwWPYMUsK_\ mIVrG1<6>S74O64K44<3>50565J69X<3>aUHiZDqc9<4>g_LeZNc\ ZP<2>YXWWWYUTY<3>NJZOMXOOZPS`PX`Q`aQd`RiZ<3>TrUTtTWu\ WYwY`z_<3>izgkzijxi<2>hqihnigmigli<3>dUidPicKicKi<3>\ _chZggYjg<3>UpfTqfTrf<4>JuiHuiFvj<3>8wk<6>JxgLxfMxf<\ 3>Sxd<5>Qm_PkZPiZ<3>ObW<2>9WMX48<3>iUJm_MpfPslSvrU<3\ >TdNM`LEYJ0RM7UHbh1<3>DXB6UEKVceWv<3>LT`FSWASQ5RLUQY\ PRVKRS<2>5VJ8WZ<3>3_O2`L1aIsbO<3>BfHDgK6hI0izojq<3>M\ nWEoQ7pLWqM<2>8tHPu5Gv98wDQxPMyN<3>9zJ6zI3zH5z62zBoz\ Y<3>QzPJzMDzK6zIjzY<3>9zJ4zt<3>2z_1zV1zQ0zLWz_<3>AzM\ 5zJfvCLzEvz_TzQFze9zj4zn<3>Fzc } 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: "Fernando Bresslau" Subject: Re: (fractint) fractal 2D/3D animation Date: 08 Aug 2000 22:17:46 -0300 Something was missing, you could tell, but now that you said so, it´s obvious. I thought we should figure it all by ourselves. Thanks, Fernando. __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.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: "Andrew Coppin" Subject: Re: (fractint) Re: 2D slices of Julibrot Date: 09 Aug 2000 13:34:39 GMT >From: "Morgan L. Owens" >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >Subject: Re: (fractint) Re: 2D slices of Julibrot >Date: Sat, 05 Aug 2000 13:53:14 +1200 > >At 07:48 04/08/2000 -0500, Johnathan Osuch wrote: >>Jim, >> >> > Four more parameter entries are >> > needed if one wishes to achieve any possible rotation centered at any >> > arbitrary point in the 4-D Julibrot object -- two entries to define the >> > remaining rotations, two entries to define initial Z. Perhaps the >> > developers will take the hint. >> >>I can add two more complex parameters easily. And will do so today or >>tomorrow. Beyond that, restructuring will be necessary. I need to be >>spending time on my job search, so the restructuring won't happen any time >>soon. > >It strikes me that it may prove worthwhile in the longer term (it would no >doubt need significant redesign, though) to allow for an arbitrary number >of parameters (p1, p2, p3, ...), rather than hardcoded restrictions. Yes indeed! >Morgan L. Owens >"But if you need 50+ parameters, you're probably trying to do too much at >once." I say again... yes indeed! ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) More 4D Slicing... Date: 09 Aug 2000 14:08:08 GMT G... what with patch 13... All those lovely parameters to play with... Must give that a try! Eeek! If the Julibrot for complex numbers is 4D... what on earth is it for hypercomplex numbers!?!?! 4D Julias and a 4D Mandelbrot... An 8 dimensional object? Too much!!! Hmm... But hey... I never really liked hypercomplex numbers. Maybe it's because they're not a proper field... maybe it's the daft appearence on the Mandelbrot... But what I really did like was the cubic Mandelbrot. Apparently (though I don't know how!) every quadratic fractal is equivalent to Z^2 + C. Go figure. But anyway... Apparently every cubic fractal is equivalent to Z^3 - 3(A^2)Z + B. Now, with each orbit determined by 2 complex parameters, both Julias and Mandelbrot are now 4D... Draw that! The real pain with the Mandelbrot though is that there are two critical point to iterate: {+A, -A}. The basin for +A is called M+, and for -A it's M-. The M set in then the intersection. Exactly how you tell fractint that is another matter (I have a formula somewhere though...) Well, I'm gonna go off and draw that... maybe... as well as all the other stuff I said I'd do... (Man! I need more free time!!!) PS. There is a Mandeloid based on the cubic Newton formula... It's like a rotated figure of 8. Anyone know the details?... ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) More 4D Slicing... Date: 09 Aug 2000 14:08:08 GMT G... what with patch 13... All those lovely parameters to play with... Must give that a try! Eeek! If the Julibrot for complex numbers is 4D... what on earth is it for hypercomplex numbers!?!?! 4D Julias and a 4D Mandelbrot... An 8 dimensional object? Too much!!! Hmm... But hey... I never really liked hypercomplex numbers. Maybe it's because they're not a proper field... maybe it's the daft appearence on the Mandelbrot... But what I really did like was the cubic Mandelbrot. Apparently (though I don't know how!) every quadratic fractal is equivalent to Z^2 + C. Go figure. But anyway... Apparently every cubic fractal is equivalent to Z^3 - 3(A^2)Z + B. Now, with each orbit determined by 2 complex parameters, both Julias and Mandelbrot are now 4D... Draw that! The real pain with the Mandelbrot though is that there are two critical point to iterate: {+A, -A}. The basin for +A is called M+, and for -A it's M-. The M set in then the intersection. Exactly how you tell fractint that is another matter (I have a formula somewhere though...) Well, I'm gonna go off and draw that... maybe... as well as all the other stuff I said I'd do... (Man! I need more free time!!!) PS. There is a Mandeloid based on the cubic Newton formula... It's like a rotated figure of 8. Anyone know the details?... ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) FOTD 10-08-00 (A Pleasant Fractal [3]) Date: 10 Aug 2000 00:07:23 EDT FOTD -- August 10, 2000 (Rating 3) Fractal visionaries and enthusiasts: Today's fractal is a pleasant one, which is the reason I named it "A Pleasant Fractal". The image is available at: and: The temperature reached 88F (31C) this afternoon. I'll be back tomnorrow. Until then, take care, and be of good cheer as you wonder. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Pleasant_Fractal { ; time=0:09:10.57 -- SF5 on a P200 ; Version 2000 Patchlevel 13 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.993309831890356/+1.652041488977905/100\ 9212/1/-45 params=10.78/-1.1/0.98/-11/0/100 float=y maxiter=1200 inside=0 logmap=145 periodicity=10 colors=000BXr5Yu<24>nhpohoqio<3>xjo<19>Q_PP_ONZM<2>I\ YIGXHGWH<24>7t47u37v3<3>6y1<7>NgJPeLRcN<3>ZWV_YW<16>\ UBNU9MU8M<3>T3K<3>kAcpBhuDmyEr<3>Zhd<13>PkYOkYNlX<3>\ LlWUU`bBd<9>PFWOGVNGU<3>IHR_AK<3>TAERADQAC<2>LA8aYBq\ tE<8>_vWYvYWw_<3>Owf<3>SqdTodUndUmc<7>`uaavabwacx`cy\ `<5>hzZizZjzZ<3>mzY<2>XzgjzT<3>ozSpzSqzS<8>Fzo } 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: "Fernando Bresslau" Subject: Re: (fractint) FOTD 10-08-00 (A Pleasant Fractal [3]) Date: 10 Aug 2000 09:35:37 -0300 Hi, Jim, but now you got me curious! compare today´s FOTD and the one in 09 July, 2000, Nothing Much. The image is the same one! Just an observer, Bresslau, Brazil http://www.fractal.art.br _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD 11-08-00 (Homespun Midget [8]) Date: 10 Aug 2000 22:12:19 -0400 (EDT) FOTD -- August 11, 2000 (Rating 8) Fractal visionaries and enthusiasts: You may have noticed that yesterday's FOTD discussion was unusually terse, and the fractal not all that outstanding. The reason was that I had saved the original and far better discussion and image on a floppy disk, to transfer the files from the Fractal Central branch office to Fractal Central itself. Somehow I lost the disk during the transport, which made me very angry. So I whipped out a new image in a few minutes, wrote a few words, and found that my Mindspring ISP was down. But all that was yesterday. This is today, and after yesterday's pathetic offering, we once again crank it up with a fractal that IMO rates an 8. The formula responsible for today's image is -1Z^(-11)-11Z^(-1.1)+(1/C), a formula that draws a parent fractal that must be seen to be believed. The parent is so unusual in fact that I might devote the entire month of September to exploring it. I named today's picture "Homespun Midget" because that phrase came to mind while I was studying the image for a fitting name. Actually, I would rather simply give my fractals numbers than attach names to them. But names do add a certain individuality to a picture, and occasionally I actually surprise myself with the poetry in a few of the FOTD names. The parameter file of today's image takes 10 minutes to render on a 200mhz Pentium, 5 minutes or less on the fastest machines. The GIF file downloads in less than two minutes. The choice of which route to take to the image is up to the potential viewer. The GIF image is available on Usenet at: and on the Web at: The fractal weather today was mostly sunny. Surprisingly, no rain fell. The temperature of 87F (30.5C) was just right for the cats. Tippy even chased a squirrel, which scampered up a tree and scolded furiously. Disappointingly, I have no fractal philosophy today. In fact, I have no philosophy of any kind. I have plenty to write about, but I just can't seem to get started. It must be a case of writer's block. Perhaps I'll get unblocked tomorrow, perhaps not. Check then to see. And even if you find no philosophy, the fractal will arrive on schedule and be worth viewing. Until then, take care, and see you soon. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Homespun_Midget { ; time=0:10:09.29 -- SF5 on a P200 ; Version 2000 Patchlevel 13 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.87822221351368700/+4.42190092650380100\ /446376.4/1/180 params=-1/-11/-11/-1.1/0/100 float=y maxiter=1600 inside=0 logmap=196 periodicity=10 colors=000mKlmKlmKjmKh<3>mKcmKbmK`<5>mFQmEOmDMmDLmCJ\ <3>j8Bi79h25<12>QLHPMHONI<3>ITM8WK<10>cPSeOShOT<2>qM\ VtLWwJZvLWuNU<2>tTNtWDtVG<2>pUNoUQnURmTSlST<2>iPUhOU\ gNTfMShLRjKQlJPlEO<3>nNGnQAnS9<5>pdFpfGphH<3>qqLywH<\ 2>mqNpvR<8>RSKOOJLLI<3>97F20C<3>B7HD9JFAKHCLKBK<15>F\ RXESYETZ<3>DXaKC5HJGFQRDXa8bo<11>KcbLcaMc`<3>QcXRfW_\ i_XoaUi_<3>ILGFFBEHG<3>DLWDN`COdCPhCQl7Pq<15>hdikeim\ fh<3>vigmqPdvD<3>arM`qO`pQ<3>YmYXm_Xma<3>UmiTmkTmm<3\ >SmuSmwSmxSmy<6>Smz } 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: "Ton Koppens" Subject: (fractint) Re: colormaps Date: 12 Aug 2000 00:17:04 +0200 Hello list, Recently I reacted to a query of Succubus for colormaps and the response was a bit more than I expected. Therefore I have set up a webpage with my collection of maps, parameters, formulas, IFS & L-system-files wich I have collected over the last years + the Fractint manual in Word format. The formula.zip is for 99% the latest orgform collection to wich were added the formulas of Greg McClure and the MMix4-Lake formulas of Sylvie Gallet. I hope the new users of Fractint have some use for these files. The url: http://members.xoom.com/ton_koppens/index.html Regards and a nice weekend, Ton 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: "Ton Koppens" Subject: (fractint) Gallery update & some pars Date: 12 Aug 2000 00:29:23 +0200 Hello list, I've updated and rearranged my Fractint galleries. The pars of some additions can be found below, I've also added zips of the pars and formulas used for download. Comments are always welcome. The url: http://home.hccnet.nl/t.koppens/index.html Regards & a nice weekend, Ton ================================================================== 00051001 { ; uses jacco293.map ; CalcTime 0:00:58.44 at 800x600 on a P166 ; Image Copyright 10 May 2000 by Ton Koppens ; e-mail:t.koppens@hccnet.nl ; Version 2000 Patchlevel 8 reset=2000 type=formula formulafile=_m.frm formulaname=ManLakefnfn ismand=y function=sin/sqr center-mag=-0.315635/0.0598998/2.60319 params=1/0.5/16/45/0.2/300 float=y colors=A0F<12>705704603602601510<11>M9COADPAE<3>VEIWFIXHJ<20>seRtfRuhS<2\ >xkTzmUylUxkTwjSwjWsfTvi_obVthbkZXsgfgVZrficR_pem_NaodpWJcmctREenfuPDbpi\ vRHcrmwZRhtpwf`mvsxdZkrnuaWimirZTgidnWQed_kUNc_VhRKaWQdOH_RLaLEX<7>SMaTN\ aUOb<2>WRdXSeWRcXUeVSbYWeVTaYYeUU_Z`eUVZ_beTWYY`cRUWWY`PRTUWZNPRSTWLMOQQ\ UJKMOORHHJMLPFFHKIMDCEGEHA9BBAC767FEGCBCJJKHGHONOMLMSSTRQRXWXWVW``````dd\ eeeeiiijjj<3>tttwwwzzz<15>NMPKJNIHK<3>76A86A<4>97E97F88H<2>98K97LA7MA6NB\ 6O<7>F3YF2ZG2_G1`H1aI0c<29>B0G } 00051003 { ; uses jacco291.map ; CalcTime 0:00:31.08 at 800x600 on a P166 ; Image Copyright 10 May 2000 by Ton Koppens ; e-mail:t.koppens@hccnet.nl ; Version 2000 Patchlevel 8 reset=2000 type=formula formulafile=_m.frm formulaname=ManLakefnfn ismand=n function=cos/zero center-mag=-0.578723/0.826177/13.84275 params=0.2/0.8/16/34/0.2/300 float=y maxiter=647 decomp=256 biomorph=1 colors=acdbceeghhilikmkknkmonnqmoqqqtoqsttwqsuwwzsuxvvyrtwuvyrtvtuxqsvsu\ xprurtworurtvnqtqstnpsprrmoqoqplnononkmmmnljlkkmjikijkhhjgijegiehicfhcgh\ aegaff_df_deYdeYcdWccXbbUbbVaaSaaT``P``R__N__PYYLZZNXXJYYLWWHXXJVUFWWHUT\ DVVFTSBUUDRQ8TSBRP8SRAQO8SR9QN8RP9PM8PN8<11>E83D73C52<2>921800911<8>KGHL\ IJMKL<2>QPQRQSQPPUUVPONWXZPOLZ`bONJUWWNMIPQPNMGKKIMLEFEALKCGE9MKCHE8OKCI\ E7PLBJE5RLBMG5SLBPI6UMASK7VMAVM8XN9aQAaTFbXKe_M<2>ljWnn_rrbtvezzf<3>haFc\ W8ZP0<2>TL0RJ0QJ0<3>MG0LF0KE0<2>HC0<4>`YJeaNifR<3>zxf<4>ZYOTSKNNG<3>000<\ 4>000<4>SRJYXNcaR<3>zxf<4>ZYOTSKNNG<3>000<4>000<4>000344000788000BCC000F\ GG556JKKBBCNOPGHIQSTMNOUWXSSUY_`XY_ } 00061303 { ; CalcTime 0:00:39.88 at 800x600 on a P166 ; Image Copyright 13 Jun 2000 by Ton Koppens ; e-mail:t.koppens@hccnet.nl ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=_m.frm formulaname=MMix4-lake-0078 function=asin center-mag=-0.05206508135169012/+0.05659432387312216/66.66667 params=0/0/45/10/0.2/300 float=y maxiter=647 biomorph=1 colors=gWVMRE<3>4A0<6>U_SXcW`g_<3>ovo<5>SZXNUTJQQ<3>3AD<6>SVcVYgZ`k<3>ll\ z<5>PSfKObGK_<3>06M<5>TZfYbibgl<3>uzz<2>uvvtuutsssrq<11>n`ZmZXmYV<2>kTQj\ SPhRO<8>SFEQECODB<2>I98G76C33700<4>SSIWYL_bP<3>pyb<6>RYINUFKQC<3>4A0<9>7\ IE7IG7JH<2>9MMANNCOP<14>adocfqegr<3>llz<4>RTiMPfILb<3>05Q<6>Y_ibclgho<3>\ zzz<15>rhgqgfqfd<3>na_m`ZkZYiYWeUT<7>RHHPGGNEE<2>H9AF78B44700<4>TRJYWNaa\ R<3>sve<6>QVI } 00072605 { ; CalcTime 0:29:43.81 at 640x480 on a 486DX 100 ; Image Copyright 26 Jul 2000 by Ton Koppens ; e-mail:t.koppens@hccnet.nl ; Version 2000 Patchlevel 11 reset=2000 type=formula formulafile=_m.frm formulaname=MandelbrotMix4 function=tan passes=t center-mag=0/0/0.6666667 params=1/-4/0.5/0.6/0.8/0.1 float=y maxiter=300 bailout=25 inside=bof60 symmetry=none periodicity=10 colors=acdKKIMLEFEALKCGE9MKCHE8OKCIE7PLBJE5RLBMG5SLBPI6UMASK7VMAVM8XN9aQ\ AaTFbXKe_M<2>ljWnn_rrbtvezzf<3>haFcW8ZP0<2>TL0RJ0QJ0<3>MG0LF0KE0<2>HC0<4\ >`YJeaNifR<3>zxf<4>ZYOTSKNNG<3>000<4>000<4>SRJYXNcaR<3>zxf<4>ZYOTSKNNG<3\ >000<4>000<4>000344000788000BCC000FGG556JKKBBCNOPGHIQSTMNOUWXSSUY_`XY_bc\ eeghhilikmkknkmonnqmoqqqtoqsttwqsuwwzsuxvvyrtwuvyrtvtuxqsvsuxprurtworurt\ vnqtqstnpsprrmoqoqplnononkmmmnljlkkmjikijkhhjgijegiehicfhcghaegaff_df_de\ YdeYcdWccXbbUbbVaaSaaT``P``R__N__PYYLZZNXXJYYLWWHXXJVUFWWHUTDVVFTSBUUDRQ\ 8TSBRP8SRAQO8SR9QN8RP9PM8PN8<11>E83D73C52<2>921800911<8>KGHLIJMKL<2>QPQR\ QSQPPUUVPONWXZPOLZ`bONJUWWNMIPQPNMG } 00072606 {; CalcTime 0:34:37.28 at 640x480 on a 486DX 100 ; Image Copyright 26 Jul 2000 by Ton Koppens ; e-mail:t.koppens@hccnet.nl ; Version 2000 Patchlevel 11 reset=2000 type=formula formulafile=_m.frm formulaname=MandelbrotMix4 function=conj passes=t center-mag=-1.06416/-0.0250522/0.8130081 params=0.5/-1/0.5/0.8/0.6/1 float=y maxiter=300 bailout=25 inside=bof60 symmetry=none periodicity=10 colors=000wuu<6>hZTfWPcTL<2>YJ9VF4SD4<3>C62842421445<4>LHBOJCRME<2>`THdW\ JfXJ<3>l_In`IoaI<12>bF8aD7`B7<2>Y54X33Y65<8>kXOm_QnbS<2>skYuo`un`<32>eGL\ dFKdEK<3>bAI000<33>H7YI7ZI7_<3>L8cM8dM8fN8gO9i<8>O9cO9bO9a<5>N9_M9ZM9ZL9\ ZL9Y<3>J8XJ8WI8V<22>426325214213112000<23>324325325<2>325436534423<7>pnn } 00080605 { ; ; ; CalcTime 0:04:24.57 at 640x480 on a 486DX 100 ; Image Copyright 06 Aug 2000 by Ton Koppens ; e-mail:t.koppens@hccnet.nl ; Version 2000 Patchlevel 11 reset=2000 type=formula formulafile=_m.frm formulaname=MMix4-lake-0169 function=atanh passes=3 center-mag=-0.78844431106694040/-0.10155693226581070/109.3974/1.2007/0/-\ 43.007 params=0/0/45/0/0.2/275 float=y maxiter=647 inside=atan decomp=256 biomorph=1 colors=`M1cG9<3>_96Z75Y54X33<9>kXOm_QnbS<2>skYuo`un`<3>sjZriYqhY<27>A868\ 75764<3>000<3>412513613714814C50<7>OA0PA0RB0SB0UC0WD0<4>YH1ZI1ZJ1<2>aN1a\ O2bP2bQ2cR2<3>eV3fW3fX3<18>urkvsmvup<2>yxwzzzzzy<18>wvVwvUwvS<2>vuNvuMvv\ OvuNvvPvvOvvQ<13>plMpkMokLojLniL<14>`O9_N9ZL8<2>WH5VF4UF4<16>B74A74964<3\ >445<4>LHBOJCRME<2>`THdWJfXJ<3>l_In`IoaI<10>dIA } 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 12-08-00 (The Pinkness of Infinity [5]) Date: 11 Aug 2000 23:40:01 -0400 (EDT) FOTD -- August 12, 2000 (Rating 5) Fractal visionaries and enthusiasts: For today's average-quality fractal it's back to the formula -1Z^(-11)-11Z^(-1.1)+(1/C), with a bailout radius of 200. As I stated in yesterday's FOTD, this formula draws a most unusual fractal, which is too large to fit on the default screen, but is worth closer examination from one end to the other. A prominent feature of this parent fractal is a large fan-shaped object. Today's scene with its unusual midget lies buried deep at the edge of this fractal fan, where chaos begins. I named the picture "The Pinkness of Infinity" mostly because I liked the poetic sound of the phrase. The 16 minutes required to render the scene from the parameter file is not so poetic however. But as always, relief is as close as the internet and the Usenet group: The image has also been posted to the Web at the URL: The fractal weather today was rather pleasant, with mostly sunny skies and a temperature of 86F (30C). The fractal cats approved of the conditions, and showed their approval by spending most of the afternoon in the yard. In the evening, when the mosquitoes got too thick, they came indoors. I did a bit of philosophical pondering this afternoon on the question of whether fractals are art, a topic that has been keeping the UltraFractal list so busy these past few days. Of course it's a futile topic, since no definite answer is possible, but it never fails to bring a flood of comments. Why, I wondered, does this one topic bring such activity every time it arises? Sometimes I feel that the UF list exists only as a forum for fractal artists to re-assure each other that they are indeed creating real art. I had assumed that fractals are art if that's what the creator intends, and that they are mathematical curiosities if this aspect is emphasized. In my case, I consider my FOTD's to lie in a grey area somewhere between art and math. IMO, It is the attitude of the creator at the time of creation that determines whether an image is simply an illustration of a pre-existing object or a newly-created work of art. If we want our fractal images to be art, then they are art. We don't need the rest of the world reassuring us that we have indeed created a work of art. If we want our fractals to be illustrations of the amazing things numbers can do, then they are such illustrations. If we want our pictures to be a bit of both, as I do, then they are a blend of art and mathematics. On the other hand, I can understand why traditional artists denigrate fractals as art. By profession I am a graphic artist. At one time, the tools I worked with were things such as a light-table, rubber cement, x-acto knife, straight edge, t-square, ruling pen, air-brush, zip-a-tone, and so on. I spent years becoming skilled in the use of these things. Then computers came. Of course, a computer now does all this tedious work far better than I ever could by hand. I don't resent computers, for they make my work far easier, but I miss the old days of 25 years ago, when it was not so easy to produce a clean and accurate camera-ready mechanical. Having spoken my bit, I find it's time to shut down the Fractal Central and call it a night. Until tomorrow, take care, believe that fractals are art, and they'll be art. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ PinknessOfInfinity { ; time=0:16:15.15 -- SF5 on a P200 ; Version 2000 Patchlevel 13 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+4.737422431714508/+0.4307302795571638/2.\ 330699e+007/1/75 params=-1/-11/-11/-1.1/0/100 float=y maxiter=1600 inside=0 logmap=299 periodicity=10 colors=000B5M<6>84K74J74J<3>54I<13>Z9f`AhbAi<3>jBplE\ rmHmhKhdNc`QZYRU<2>YUFYVG<3>YZQY_SY`UYaXYbZWdb<5>bVW\ dTVeSUfQTgPShNRjKP<16>afXagY`iY<3>Zn_OnWbo_km_<3>e`l\ dXpeUsfRvgPx<5>mKynJyoIzpHzqHz<3>xDzzDzwCx<3>kCshCqd\ Cp<8>PBdNBcLBa<2>GBYEBXB8V<12>QadRceSef<3>Wnh<3>9fI4\ hB<6>4QF4NG4LH<2>4DI4AJ26A<2>8CZ6DhAEfDFe<3>VI`ZJZcK\ YhLXnLYjLWfLUaLSXLQ<4>LLGJLEGLC<3>7L4PHk<2>_Znccr<12\ >RmPQnMPoK<3>LrBGs8<3>VvBYwCaxC<2>kzEbzEUzMLzU2zV<2>\ UznHzQ<8>CzM } 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: "S. Wyszkowski" Subject: Re: (fractint) FOTD 12-08-00 (The Pinkness of Infinity [5]) Date: 12 Aug 2000 01:14:31 -0400 Let me make a brief addendum to Jim Muth's remarks of August 11 (with which I agree): Fractals, per se, arise entirely automatically out of certain algorithms. Whether they be art or not, their creation involves no artist, except in so far as a particular algorithm may be consciously and knowledgeably chosen with an artistic purpose in mind. The artist appears when a particular segment of the fractal image is selected for aesthetic reasons ("found art") and again when the selected segment is consciously modified to suit artistic purposes at which point it may cease being a fractal (and become art?). S. W. Paul Wyszkowski Images Invented and Discovered swpaul@earthlink.net ----- Original Message ----- Cc: Sent: Friday, August 11, 2000 11:40 PM> > > I did a bit of philosophical pondering this afternoon on the > question of whether fractals are art, a topic that has been > keeping the UltraFractal list so busy these past few days. Of > course it's a futile topic, since no definite answer is > possible, but it never fails to bring a flood of comments. > > Why, I wondered, does this one topic bring such activity every > time it arises? Sometimes I feel that the UF list exists only > as a forum for fractal artists to re-assure each other that they > are indeed creating real art. I had assumed that fractals are > art if that's what the creator intends, and that they are > mathematical curiosities if this aspect is emphasized. In my > case, I consider my FOTD's to lie in a grey area somewhere > between art and math. > > IMO, It is the attitude of the creator at the time of creation > that determines whether an image is simply an illustration of a > pre-existing object or a newly-created work of art. If we want > our fractal images to be art, then they are art. We don't need > the rest of the world reassuring us that we have indeed created > a work of art. If we want our fractals to be illustrations of > the amazing things numbers can do, then they are such > illustrations. If we want our pictures to be a bit of both, as > I do, then they are a blend of art and mathematics. > > On the other hand, I can understand why traditional artists > denigrate fractals as art. By profession I am a graphic artist. > At one time, the tools I worked with were things such as a > light-table, rubber cement, x-acto knife, straight edge, > t-square, ruling pen, air-brush, zip-a-tone, and so on. I spent > years becoming skilled in the use of these things. Then > computers came. Of course, a computer now does all