May 2002 - Fractint - mailman.xmission.com

Re: [Fractint] FOTD 30-04-02 (Frenetic [7])
by M J Benkers 13 May '02

13 May '02

>Being colored with the outside=tdis option, Well, the version of Fractint (20.0) that I use, doesn't know this option! Mary

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FOTD 12-05-02 (Galactic Arm [7])
by Jim Muth 12 May '02

12 May '02

FOTD -- May 12, 2002 (Rating 7) Fractal visionaries and enthusiasts: With today's image we embark on a trip to interstellar space. It's enjoyable to be able to do this on a computer, since the way man is going, no one will ever be able to do it in person. (We won't lack the know-how; we'll lack the resources.) Our trip takes us to an arm of the local galaxy -- let's call it the Orion arm -- from where we see ourselves surrounded by clouds of nebular gas and nascent stars. All around us is a vast emptiness. Yet the emptiness is not the nothingness that it first appears to be, (vacuum energy?), for on this trip we have been given additional senses. We have the senses to perceive magnetic fields as well as gravitational fields. Since these new perceptions would likely appear to us in a manner we cannot now imagine, I have translated them into vision, which we can imagine. So, in my fancy, today's image, dark and somber as it is, shows the star-lanes and energy fields of a very densely populated area of our Milky-Way Galaxy. With this in mind, I named the picture "Galactic Arm". The rating of a 7 is optional. Actually, the image is one of an 'evaporated' midget, which has ceased to exist, but whose ghost has been revealed by illumina- ting it with the ghost-busting <bof60> inside fill. (A <fmod> fill would also have worked.) The very simple fractal formula Z-(1/Z)+(1/C) created the original midget, which I killed when I raised the escape radius to one-googol plus one-hundred. (The one-hundred is built into the M-Mix2 formula, though it has no effect on the final result.) The bad feature of images such as today's, which consist totally of trapped inside points, is their slowness. Today's image requires over an hour to render on my tired old P200 machine. It will render faster on a state-of-the-art screamer, but the easiest way to see the image is to let Paul and Scott do the rendering and download the completed image from either of their web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather, (Is there any other kind?), Saturday here at fractal central was ideal. What could be better than a temp- erature of 73F, unless it was a temperature of 22.75C? The cats spent the entire afternoon in the sun of the yard, frolicking like tired kittens. And no, Tippy did not catch any more sparrows. As for myself, it's Sunday, it's Mother's day, and I'm going to treat myself to a well-deserved rest from work on both the CD and the stuff that I expect to bring profit. But I still might sneak in a fractal or two when the obligatory social activity has been accomplished. Regardless, until next time, take care, and try to decide whether fractals are really real or are real merely because we decide they are. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Galactic_Arm { ; time=1:10:15.64--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.65751903104643300/+1.790625615929802\ 00/100087.5/1/-152.5/-3.13505964244509272e-009 params=1/1/-1/-1/0/1e+100/0/0 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 sound=off colors=000uiqrhoogmlfliekfdiccgabeZacX`aV__SZYQYWO\ WULUTJSSGQSEORJAMJ9K00800B00D00G00J00L00O00R00T00W\ 00Z00`00a00b00c00d00e00e00f00g00h00i00j00j00k00k00\ k00k00l00l00l00l00l00m00m00m00m00m00h00c00_00V00Q0\ 0M00W00e00o00l00i00f00c00`00Y00V00S00P00M00P00R00T\ 00V00X00Z00T00O00I00D00800C00G00J00N00R00U00Y00a00\ d00h00l00o00m00k00i00g00e00c00a00_00Z00X00W00V00U0\ 0S00R00Q00P00O00N00M00L00K00J00I00H00G00F00E00D00C\ 00B00A00C00E00F00H00I00K00L00Q00V00_00d00i00n00s00\ w00r00n00j00f00b00Y00U00Q00M00I00E00m00o00q00g00Y0\ 0Z00_00_00`00a00a00b00b00i00g00e00c00a00_00Y00X00Z\ 00_00`00a00b00c00d00f00g00h00i00j00k00l00k00k00k00\ k00k00k00k00k00k00f00a00X00T00O00J00F00A0050010070\ 0C00H00M00R00W00a00f00k00p00u00z00t00o00j00e00_00V\ 00Q00L00G00F00F00F00E00E00E00I00L00O00R00V00Y00`00\ c00g00j00m00p00s00`00J00M } frm:MandelbrotMix2 {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Mandellace
by M J Benkers 12 May '02

12 May '02

A new picture from the Netherlands! It's made with cubic in the fractint.frm file (9.48.68 on a Pentium 200). By the way, there are a lot of nice pictures to construct with this formula. Mary Stultorum infinitus numerum est. mandellace { reset=1910 type=formula formulafile=fractint.frm formulaname=Cubic center-mag=-0.02295512076302016/+2.845707937164529 00/1.76006e+007/1/-32.\ 499 params=0/0/0/0/0/0 float=y maxiter=5000 inside=0 colors=000KKa<4>MMeNNfOOg<28>ggxhhxiiy<28>xxzxxzyy zyyzzzz<28>zcczbbzaa<4\ >xYYxYYwXXvWW<21>iFFiEEhDD<30>M11L11K00<25>4003002 00200100<3>001002113<2\ 3>66I66I66J<24>JJa }

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homemade watch
by Bill Jemison 10 May '02

10 May '02

I always thought that it looked like some naked guy sitting on the scanner. <Interesting ... it doesn't really look _that_ much like a person, but <it's quite frequently described as one - apple-man, it seems; or snowman <(with an aerial sticking out of his head) - even though the figure has <to be turned on its side from its convenetional orientation for the <description to make sense!

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Re: [Fractint] Mary Benkers, New person on the list
by M J Benkers 10 May '02

10 May '02

> I liked your picture in the M-set very much Don't ask me how I made it! It can't remember what I did to make it, it's too long ago! Mary

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FOTD 09-05-02 (Spider-Man Delbrot [7])
by Jim Muth 09 May '02

09 May '02

FOTD -- May 09, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal has been created by iterating the deceptively simple fractal formula -1(Z)-(1/Z)+C, an expression that at first glance would appear to result in no fractal at all when iterated. But things are not always as they appear in the world of fractals, and today's image is a perfect example of the ability of fractals to create something from nothing. I named today's image "Spider-Man Delbrot". The spider-web effect around the central midget inspired the name. The new Spider-Man movie likely played a part also. I decided to give the image a rating of an above-average 7. Whether this rating is deserved is up to the individual to decide. In this particular image I departed from the usual FOTD equal- iteration-band outside-coloring algorithm and tried the alternate outside=summ. The result was not much of an improvement, but the improvement was enough to cause me to temporarily change my usual coloring method. The parameter file renders in 19 minutes on a quaint old P200 machine. The image file downloads from Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> in far less time. The news for those waiting with bated breath for the FOTD CD to appear is good and bad. The good news is that the CD is making progress; the bad news is that I continue to find new things that need to be done to make the disk easy to use. The latest task is to change the names of the fractal image files from their present cryptic 8-letter DOS names to names which are the dates on which the images appeared. I can either change the names of the image files or place every day's discussion and image in a separate directory (folder). Right now, the files are organized into monthly directories. Whatever I do, the time required will be several additional days. Take a couple dozen of these unanticipated 7-day tasks and it's easy to see why the CD is taking so long. The fractal weather Wednesday started sunny and mild, but as the afternoon progressed, the clouds moved in. The temperature of 70F 21C must have been just what the cats ordered, because they spent most all day romping in the yard. Tippy set the day's high point when he showed up at the door with a sparrow in his mouth. This was the first bird he has caught in over a year. There's life in the old ex-tomcat yet. Now if Thomas can only catch something other than a ray of sunlight. . . . As for me, I've got work to do, both for money and in the preparation of the FOTD CD. The time will never be better to get started, so until next FOTD on May 12, take care and be happy. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Spider-Man_Delbrot { ; time=0:18:52.84--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+2.010171243979102/+0.1046890830356033/\ 106079.2/1/167.5/2.3982375016440294e-008 params=-1\ /1/-1/-1/0/525 float=y maxiter=1400 inside=0 outside=summ colors=000GFZUqhRnYQlOOjFNh5SZ0Qa0Nd0\ 0RJ0QM0OO0NQ0NS0MV0KX0JZ0Ia0Gb0Fe0Eh0Ci1Bl19n18p17\ s17t08s08q08p08n08m08l08j08i08h09h09f09e09d09b09a0\ 9`09Z09Y09X0BX0BV0BU0BS0BR0BQ0BO0BN0BM0BM3EO7GRBJU\ FKXKNZOQaSRdXUfaXieYli`nmbqqdssiism`sqRqmOpiNneMma\ KlYJjVIiRGhNFfJEeFCdCBeJ9fO8hU7hZ5id4ji3ln1lt1iu0h\ u0fw0ew0dx0bx0ax0`y0Zy0Yz0Xz0Vz0Uz0Sz0Rz0Qz0Nz0Mz0\ Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz09z08z07z05z04z03z05z18z49w\ 7Cs9EmBGiEIdGK`JMVMORNQMQSISUCVX8YY4ZZ8aZCd`Fe`Jha\ MiaQlbSmbXpdZqdbtdeuIXl0Nb0Md0Kd0Kd0Jd0Jd0Id0Id0Gd\ 0Gd0Fd0Fd0Ee0Ce0Ce0Be0Be09e09e08e08e07e07e08b08a09\ `09Z3BY4BX7CV8CU9ESCEREFQGFOIGNKGMMGKNIJQIIRJGUJFV\ KEYKCZMB`M9bN8dN7fO5hO4jQ3lQ1mQ0nS1pV1qY1s`3tb3ue3\ wh4xj4ym4zp5zs5zu5zx7zz7zz7zz8zz8zz8zzEzzIzzMzyQzw\ UztYyqaxnewliuimtfqsduqayp`zpaqpbfpbXpdMpdBtbGwaMy\ `Rz`VzZ`zYezYilXSQVB3U0Qe39Z0Gb0YZdRbI } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Mary Benkers, New person on the list
by Harold Lane 09 May '02

09 May '02

Mary, I am new to the Fractint list also - although I wrote a lot of programs to create fractals back when the graphics adapters commonly had a resolution of 320 x 200 with 16 colors! I am enjoying getting back to creating fractal images using Fractint. I liked your picture in the M-set very much. It has a nice Julia set-like quality to it. I especially liked your color map. It is very sophisticated - despite its apparent simplicity. How did you make it? One unusual aspect of your image and color map is that the mostly red outside edge of the 'island' of your image is adjacent to a blue surrounding field. Due to the fact that the eye focuses different colors at different depths in the eye, the 'island' in your image appears to hover 'above' (closer to your eye) than the blue surround. You have created a truly three dimensional image - as far as the eye is concerned! (This effect is enhanced somewhat if the room you view the image in is darkened and direct your gaze to the boundary between the red and blue. When the effect appears I can then refocus my attention to the entire island and it will remain hovering above the blue 'background'. ) Did you construct your color map in order to create this effect? Please let me know whether you are able to see this effect. Would others who create your image please let me know whether they can see this as well? Thanks I zoomed into the center of your image on the miniature mandelbrot set located there (Jim Muth calls this a 'Midget') and created another image using your color map. The file to create it follows. The image takes about 3-4 hours on a P400 using the 1024 x 768 x 256 disk video mode. (My Windows 98 machine actually uses Expanded Memory instead of the disk.) I increased the maxiter to 10,000 to insure an accurate coastline to the mini-brot. I don't believe that the high maxiter is the cause of the long creation time. I believe it is because in most of the image the actual number of iterations it takes to color the pixel is large. Also, periodicity testing inside the 'lake' of the M-set should keep the number of iterations from reaching 10,000 there. [Can anyone confirm those two conjectures?] The 'island' in my image resembles a starfish with eight arms. Just within it is the outline of another 'starfish' with 16 arms. Within it is one with 32 arms, etc. I can just begin to make out some of the arms of the starfish with 256 arms with the image rendered at 1024 x 768. I don't recall being able to see a period doubling of that high an order before - and I look every time I see this doubling in a minibrot. I believe that Guy's expression in his message to you: "...a more performant version of FractInt..." means that it will create images more quickly. :-) - Hal Lane USA mandelischia_midg{ ; Zoomed into the center of mandelischia_coli.par ; Orig par by Mary Benkers NL, midget by Hal Lane USA ; Fractint Version 2002 Patchlevel 3 (20.02.3) reset=1910 type=mandel passes=1 center-mag=-1.8605739577363196/-9.3407056855e-7/8.742819e+012 params=0/0 float=y maxiter=10000 inside=0 distest=1/71/1024/768 sound=off colors=000uux<2>xxyzzzyyz<42>GJeFIeEHdDGdBEc<25>BCOBBOBBN<2>BBLAAKCDK<8>\ YcF_fFaiE<3>kuC<9>OSHMPIKMI<3>AAK<9>f48i36m35<3>z00<9>zbbzffzjj<2>zvvzzz\ xvw<6>mRbkN_jIX<3>c0K<5>l8Hm9GoAFpBErDE<3>xIBzKAzMB<8>zjMzlOzoP<3>zzU<9>\ TVYQSZNPZ<3>9C`ADaBEc<42>ttw } >Hello, > >I am new on the list. My name is Mary and I am >from the Netherlands. >I hope you do like my picture. It is somewhere on >the Mandelbrot set. It takes 6 min on my computer >(P200) to make it. > >Mary Benkers > >mandelischia_coli { ; some strange bacteria? >reset=1910 type=mandel passes=1 >corners=-1.8605739577489129/-1.860573957723912/-9.3407929358274632e-007/\ >-9.340605428307932e-007 params=0/0 float=y >maxiter=1500 inside=0 >distest=1/71/1280/1024 >colors=000uux<2>xxyzzzyyz<45>DGdBEcBEc<29>BBLAAKCDK<14>kuC<15>AAK<15>z00\ ><15>zzz<12>e5Oc0Kd1K<12>xIBzKAzMB<14>zzU<15>9C`ADaBEc<42>ttw > }

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Re: [Fractint] homemade watch
by Mark Christenson 08 May '02

08 May '02

At 03:39 PM 5/7/02 -0700, John wrote: >... >I also found a "fractext.exe" on a German site. The automatically-translated page said: > >"Fractal of extremes provides and stores bizarre and apparently coincidentally developed Fraktale in form of the well-known apple males over mathematical almond bread functions in different dissolutions. With the mouse you click a range of the Fraktals, which is then gezoomt and again computed. (Shareware, English)" > Fraktale: presumably Deutches for "fractals". apple males: not sure about the males, but the word for apple (apfel) also means "ball". Maybe it works out to something like "spherical projections" ;-) almond bread: literally "mandel brot". Now you know what his name *really* is! dissolutions: probably "resolutions". Glad to be of service, Bud

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FOTD 06-05-02 (A Broken Minibrot [5])
by Jim Muth 06 May '02

06 May '02

FOTD -- May 06, 2002 (Rating 5) Fractal visionaries and enthusiasts: The parent fractal of today's image was created by the iterated formula Z^(1.8)+C, and is shaped like a rotated and perturbed version of the classic M-set. The image is located in a broken elephant trunk of the fractured East Valley area of the parent. I named the image "A Broken Minibrot" because of the spirals which are so obviously broken. The image is of average quality and rates an average rating of 5. The breaks in image continuity are unavoidable with fractional exponents of Z, and are caused by the multi-valued nature of the complex log function. But the same multi-valued nature is not all bad, since it makes the resulting fractals infinite both on the surface as well as in their depth. The 14-minute render time can be reduced to a minute or two by going online and downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though I took the day off on Sunday, the FOTD CD is progressing. A midsummer completion still looks likely, and anything worth having is worth waiting for. The all-important fractal weather Sunday here at Fractal Central was just what the fractal cats ordered. Well, maybe they didn't order it, but they certainly did enjoy it. Warm sun, light winds and a temperature of 68F 20C made conditions ideal for man and cat alike. Both the dynamic duo and myself spent a good part of the afternoon in the yard, the only diversion being when Tippy started rolling in the emerging catnip patch. Since all good things must eventually end, this day is just about on its last lap. It's near late-news time and I can't end the day without knowing the latest bit of bad news. So until next time on May 9, take care, and let's get some fractal into that fractal philosophy. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Broken_Minibrot { ; time=0:14:36.56--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.00817267703828271/+0.240493666992600\ 80/1.818109e+011/1/114.999944662658265/-1.10636886\ 913803578e-005 params=1.8/0/28.7/0 float=y maxiter=4500 inside=0 logmap=366 symmetry=none colors=0009F04D06F07F09F09G0AG0CG0DI0DI0FI0GJ0IJ0I\ J0JL0LL0LL0MM0OM0PM0PO0SO0VO0VP0WP0XP0XQ0YR0YS0ZS0\ ZS0ZS0YT0ZS0ZT1XV4VX7TYAQ_DP`GOaJLcMJdPIfSGhVDj_Cl\ aAmd7og6pj4rm1sp0us0vv0xy0yz0zz0zz0zz0zz0zx0zu0zr0\ zo1zl3zi4zfAzXGzOMzFSy6Yu0cr0do0fm0gl0gj0ii0jg0jf0\ ld0mc0ma0o_0pY0pX0rV0sT0sS1uQ3vP3xO4xM4yL6zI6zG7zF\ 7zD9zC9zAAz9Az7Cz6Cz4Dz0Cz3Dz6Dz9FzCFxFGuIGrLIoOIl\ QJiTJYSMaTLfVJjVIoXGsYGxYFz_Dz`Czg6zc9z`CzYDzVGzSI\ zPLzMMzJPzGSyDTyAXx7Yv4`u1as0dz0gs0fg0dY1cM4aA6fC7\ cC7aD9`D9YFAXFAVGCSGCQICPIDMJDLJFJLFILGFMGDMGCOI9O\ I7PJ6PJ3QL1QL0QL0OJ7LIGIGPGGgDFvADz3Cz6Dz9DzCDvDDo\ GDlJDgLDcOD`QFXTFTTFPTFLTFITFDTFATF6TF3YTSacu_foXi\ jTlfQo`OrXLuSIvOJvPJvPLvPLvQMvQMvQOxQOySPzSPzSQzTQ\ zTSzTSzVTzVTzVVzXVzXXzXXzYYzYYzY_z__z_`z_azY`z_`z_\ `z``z``za`za`za`zc`zc`zd`zd`zd`zf`zf`zg`zgMzJMzOLz\ QLzTLzXJz_JzcIzfGz4Dz3Cz1 } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 03-05-02 (Eight Gold Keyholes [6])
by Jim Muth 03 May '02

03 May '02

FOTD -- May 03, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal scene exists in an oversized parent fractal, way out on a filament that leads from a mandel-bud of the main bay and terminates in a ring-like feature. Many filaments converge on this ring, but only the one that comes from the bud has midgets along it. The terminal ring is mirrored in the eight rings, (I call them keyholes), that surround the midget in today's image. The formula of the parent fractal is Z^(-11)+6Z^(-1.1)+(1/C). This formula was iterated by the MandelbrotMix2 Fractint formula, which likely will replace the old M-Mix4 formula as my most often used formula. The speed of the new formula is the same, and the new one is more versatile. The blue-gold color scheme makes the image appear a bit better than its actual worth of average. I therefore rated it at a 6, which is the least possible above-average rating for a FOTD fractal. The 9-minute render time of the attached parameter file makes a download of the completed GIF image the marginally better choice. That download can be found at Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday started with a heavy thunder-storm, followed by sun from 10am to 3pm. At 4pm, another heavy thunder- storm, this one with golf-ball-sized hail, passed over. Between storms it was warm and humid, with a temperature around 80F 27C. The fractal cats found enough time during the midday sunny period to romp in the yard, but when the hailstones started clattering, they dashed for cover and didn't come out for nearly an hour. As for myself, I've got work waiting and not enough time in which to do it. The best way I know of solving the problem is to get started, so that's what I'm about to do. And that FOTD CD, which has been languishing of late, still has a considerable amount of work to be done. The next FOTD will appear May 6. Until then, take care, and be philosophical. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ EightGoldKeyholes { ; time=0:09:07.33--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+428.8990414983479/-46.07822226439/272/\ 1/-15/-6.55149697686985277e-009 params=6/-1.1/1/-1\ 1.1/0/525/0/0 float=y maxiter=1500 inside=0 logmap=149 periodicity=0 colors=00000l00m00n01o02p\ 03q04r05s06t07u08v09w0Ax09y07z05x05z03u03x03r03q01\ m01j01f01d00a00Y10U10Q10N30J30F30D3095055015007007\ 00700700B00F30H70LB0PF0QL0UP3YS5ZW7cZBfdDhhFllJooL\ qpNrqLsqLtqLuqLvqLwqLwqLwoLwoLwoLroLroLmoLmoLmmLmm\ LmmLmmLimLimLfmLijNjhPlfQmdQoaSqZUsYUtWWvUYyQYzPZz\ NazLazJczFdzDdzBfz9hz7hzBjzFlzHmyLovPqsQqoUslYthZv\ dcxafyYhyUlzQozNqzJtzFxzByzDzzDzzDzzDzyDzvDztFzsFz\ qFzmFzlFzjFzhDzjBzlBzl9zm9ym7vo7sq5oq5ls3hs3dt1av1\ Yv0Ux0Qx0Ny0Jy0Fy0By07y09v0Bs0Do0Fl0Hh0Jd0Ja0LY0NU\ 0PQ0QN0SJ0UF0UB1YF1aP3dY5hf7loFoxNszUvzayzhzzfzzdz\ zdzzczzazzazzYzzUzzQzzPzzLzyHzyFzxBzx7zv5zv7zo9zhB\ taDmUFfNHaFJc7Ld0Nf0Ph0Pj0Sl0dm0fq0ht0jq0lo0mm0oj0\ qh0sf0tc0ta0vZ0xY0yY0zY0zY5zYFzYJzYNzYQzYUzYYzYazY\ dzYhzYlzYozYszYvzYyzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzz\ YzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYz } frm:MandelbrotMix2 {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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