June 2002 - Fractint - mailman.xmission.com

Re: [Fractint] Kleinian Group formulas - Pars (and) More pars
by Sylvie Gallet 08 Jun '02

08 Jun '02

Hi Gerald, >> That's the first time I've seen images by you *and* knowing beforehand >> the formulas they are based on (therefore probably having formed a kind >> of preconception what kind of pictures I could expect). I haven't posted any image in a while... >> Needless to say your images were a 100 percent surprise. :-) Thanks for the formulas. Here's a couple more pars: m5KLN04 { ; . t= 0:04:08.38 ; Copyright Sylvie Gallet, May 28, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=Mod5Klein_Group passes=1 center-mag=-0.714769/1.47741/11.17785/1/-27.500000000000032/\ 3.85524945301085609e-014 params=25/1/3.5/2/5/5/5/0 float=y maxiter=1000 inside=0 proximity=2 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=Wab<27>hlohloimp<3>jnqjnqjnq<6>imoimoimo<3>hlnhkngkn<\ 108>QTTQTTQTTQTSPTSPTS<79>CGCBGCBGB<3>AFAAA0<2>K00 } m5KLN05 { ; . t= 0:02:55.71 ; Copyright Sylvie Gallet, May 28, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=Mod5Klein_Group passes=1 center-mag=-0.91962/2.94147/1.470554/1.1205/137.802234114105\ 147/-0.571944980072052411 params=5/2.5/3.5/2/5/5/5/0 float=y maxiter=1000 inside=0 proximity=2.1 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=hloWab<26>hlohloimp<3>jnqjnqjnq<135>TXWTXWTXW<70>CHCC\ HCBGC<3>AFAFA0<2>K00 } Cheers, - Sylvie ----------------------------------------------- E-mail: Sylvie_Gallet(a)CompuServe.com Web site: http://www.fractalus.com/sylvie/homepage.htm -----------------------------------------------

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Re: [Fractint] FOTD 30-05-02 (Mandelbrot Atom [6])
by Multiple Bogeys 07 Jun '02

07 Jun '02

>The weather here at Fractal Central was near perfect Wednesday. >Only a bit too much humidity kept it from being absolutely >perfect. The brilliant sun and temperature of 82F 28C was ideal >for any activity including sleeping, which the fractal cats did >most of the day and which is not exactly an activity. But they >did it anyway, and they did it well. More like an inactivity. :)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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Re: [Fractint] Fwd: Ikenaga Fractals???
by Multiple Bogeys 07 Jun '02

07 Jun '02

>The reason you iterate z = 0 with the quadratic is that it's a >critical point of f(z) = z^2 + 1. By analogy, for the cubic you >should iterate the critical points (plural) and (I hope I don't >screw this up!) see if *at least one* escapes. (If I'm wrong, >then you see if *both* escape; unfortunately, I know nothing >about dynamics. As I said, I don't work in the area!) The >derivative for the cubic is 3z^2 + (c - 1). So you need to set >this equal to 0 and solve for z (which gives two complex square >roots, which gives two critical points). You iterate these >guys, not z = 0. Thus, you'll be iterating different points, >depending on the current value of c. In these kinds of situations I have my computer study the fate of both points, and plot distinct color gradients depending on what pattern occurs. The results can be quite spectacular. With Ultra Fractal there's a nifty trick. Make a formula, and make the critical point selection a parameter. Generate a two-layer image with each layer having the same settings save critical point selection. Give them distinct outside gradients. Then you can get, say, black where both points are trapped, dark gradients where one escapes and a different shade depending on which, and where both escape, a colorful gradient that has filaments of two different colors present. Inside Mandelbrot-like regions can be found dendrites studded with filled-in Julia set like forms, as well as more mini Mandelbrots, in black; the Julia like forms have both critical points sucked into the same attractor, and the smaller Mandelbrot figures have them going to separate attractors. Of course, it gets hairier with quartics. Then there are three critical points... >Feel free to copy this to others if it helps to correct this. >Oh ... do any of those fractal-generating programs actually do >the cubic, but the *correct* way? If not, you could do a favor >for the people who write these things by letting them know. Well I have both Fractint formulas, Ultra Fractal formulas, and C code that produce generic cubic images. They use the two-parameter cubic family z^3 - 3a^2z + c, however, with critical points +/-a. >(Maybe go ask a dynamical systems person first whether you want >*at least one* or whether you want *both* critical points to >escape in order to color the point c. Don't take my word for it >--- as you can see, I'm not a good source for this!) This depends on what kind of picture you want to generate. The usual rigorous Mandelbrot analogue is the set where all critical points are trapped. For all polynomials, this set is connected, though you may be looking at a space with a large number of parameters. For each critical point you can get interesting fate maps. To really have a map of the full dynamic behavior of the function, though, you need to do the Ultra Fractal layering thing. (In particular, the high-iteration stuff of different critical points should get distinct colors, which means layering with different gradients.)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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FOTD 06-06-02 (Stems [6])
by Jim Muth 06 Jun '02

06 Jun '02

FOTD -- June 06, 2002 (Rating 6) Fractal visionaries and enthusiasts: Take four lines with a length of -1 meter and arrange them as the sides of a square. The result is a square with an area of one square meter and four sides that measure one meter less than nothing. This is not only getting something from nothing; it is getting something from less than nothing. Then take six of these square meters with sides less than zero and arrange them as the sides of a cube. The result is a cube with a volume of one cubic meter less than nothing. I shall not attempt to describe this incredible beast, but I shall note that if eight of these weird cubes were arranged as the cells of a 4-D hypercube, that unimaginable object would have a hypervolume of 1 quartic meter more than nothing. This situation is mathematically correct, though I have yet to see a line with a length of -1 meter. It simply shows that much mathematics extends far beyond the everyday world in which we live. I have also never seen a real-life fractal, though I have seen hundreds of thousands of pictures of fractals. Today's image simply adds one more fractal picture to the ever-growing list. The image is a scene in the fractal created by the formula (Z^3)+0.4(Z^5)+C. I named it "Stems" because of the sprawling stem-like features surrounding the midget at the center. Like so many other recent FOTD images, today's image rates a nominal 6. The render time of 2 minutes makes running the parameter file not too great a task. And as always, the GIF file of the completed image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday was very warm and muggy, with a temperature of 92F 33C and humidity to match. In the late afternoon a very noisy thunder-storm developed, which sent the dynamic duo of fractal cats scurrying for cover. They stayed out of sight until hunger brought them into the open around nightfall. As for myself, as is normally the case, I've got too much work to do and too little time in which to do it. The remedy for such a situation is to get busy and resume productive activity. So until Sunday June 9, take care, and be of good humor. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Stems { ; time=0:02:48.18--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+0.54332395099606500/+0.517188441425538\ 80/1.244136e+010/1/-67.5000495545287009/7.69023680\ 009528476e-005 params=1/3/0.4/5/0/0/0/0 float=y maxiter=300 inside=0 logmap=49 periodicity=10 colors=000HfuHcqH`lHYhHVcHS_HPVHNTHLRHIQKFPNHNQKNT\ NOWQQZTR`XSg`RmeQtkPzpOykQygRxcTx_UxWWwSXwPZvL_vIa\ vFbuCdu9et6gt3ht0ip8fmGdiOafW_cbYbaZa`Z`_Z___ZZ_ZY\ _YX`XX`WW`VVaUUaUUaYYY`aVcdRfhOjlKmoHpsDsvAmwFgxJa\ xOWySRyWDlT0_R6ZMCZHHYDNY8SY4TZBT_HT_NT`UU`_UaeUal\ UbrUbxVcrWclXcgYcaZcX_cR`cMacGacBiiDqoFyuGwpFulFsh\ FqdFo`FnXFlTFjPFhLFfHFeDF`KKWRPSXUNcZJibGk`DmZBoY8\ qW6rV9pXCoYEn_Hl`JkbMjcPheRgfUfhWdiZckablc`nf_ohZp\ jVqlRrnOrpKsqHsrFprEnsDlsCjtAht9fu8cu7av5_v4Yw3Ww2\ Uw1SuNHth7ti9tjBtkCtlEtmFtnHtoItoKtpMtqNtrPtsQttSt\ uTtvVtxWhzaYzfNzkCzpRzbezPtzBrzDqzEpzFozGnzHlzIkzJ\ jzKizLhzMgzPfzRfzTezVezXdzZdz`czcczebzgbziazkazm`z\ o`zqYzjVzdSzYPzSMzMJzFGz9Dz3Fz8GzCIzHJzLLzQMzUOzZP\ zbRzgSzkTzoVzkWzgYzcZz`VzaRzbNzcJzdFzeBzf7zg3zgGz`\ TzVezPdzQdzRdzSazQ_zOXzNVzLSzKQzIOzHLzFJzDGzCEzABz\ 99z77z6FzHNzSVzaWzROzhHzz } 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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Kleinian Group formulas - Pars (and) More pars
by Sylvie Gallet 04 Jun '02

04 Jun '02

I4KLN07 { ; . t= 0:02:52.14 ; Copyright Sylvie Gallet, Jun 03, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=47.4891/-37.7833/0.4930351/1/-80.0000000000000995\ /1.40332190312619787e-013 params=1.1/2.2/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=PCZPD_<3>PLhPMkPOmPQpPSs<5>WhvXjwYmw<2>`vybyzeyz<3>sx\ zwwzxxzzzz<6>sswrrvqqv<7>kkpkkojjojjo<12>``d__cZZb<13>QQTPPS\ OOR<11>IILIILHHK<23>BBDAACAACAABAAB<8>889889778<108>11111111\ 1<3>000U0F<2>R5QP7UP8VPAX } I4KLN08 { ; . t= 0:01:22.29 ; Copyright Sylvie Gallet, Jun 03, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=1.31098/-0.214135/4.645177 params=2/4/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=K0A<2>L3GL5JL6LL8NL9P<5>NJaOLcOMf<2>PRlPTnQVn<4>WgsYi\ tZlu<2>bsxcvydvy<4>lvxnvxovw<3>vvv<62>FFIEEHEEGDDGCCF<28>222\ 222111<98>000000000<3>000<8>zzz } I4KLN09 { ; . t= 0:05:22.85 ; Copyright Sylvie Gallet, Jun 03, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=0.108716/-1.47678/2.654569/1/-55.0000000000000924\ /-1.23373533611470521e-014 params=3/4/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=tttzzzzzc<3>kqahoadm`<3>PcZ<3>VfcXgdZhe<10>nqrorsqsu<\ 2>uvxwwzwwz<58>dgidgidgicfhcfh<7>X_aWZ`VYZ<3>RUVQTUORS<36>IK\ LIKLIKK<8>FIIFIIFIIFHHEHHEHH<48>233233122<25>111111111<3>000\ <3>zzz } I4KLN10 { ; . t= 0:06:34.10 ; Copyright Sylvie Gallet, Jun 03, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-0.955661/-2.12297/1.581048/1/-57.500000000000149\ 2/3.88578058618804789e-016 params=3.2/4/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=000vxc<3>hoadm``k`<2>PcZ<11>gmlhnmjon<3>orsqsurtvtuwu\ vxwwz<3>vvyvvyuvy<3>uuxuuxttx<59>`ci`ci`ci_bh_bh_bg<69>BEFBE\ EBEE<2>9CC9BB9BB9BB<10>688677577<44>111111111<3>000PPRmmqwwz } I4KLN11 { ; . t= 0:14:12.89 ; Copyright Sylvie Gallet, Jun 03, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-2.58037/-3.90689/1.534359/1/-65/1.31075705844807\ 544e-014 params=4/5/1.05/1 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=krC<3>zzz<16>aer_dqZcq<2>U_oTYnTXl<7>PKbOI`OH_<2>MCWM\ BVLBT<9>J4GI3FI3D<2>H19H08I07J07J06<22>bE2cF2dF2<27>vl1vm1wo\ 1<2>yr1zt2yt2<17>`b4_a4Y`4<5>RW6PV6OV6NU6MT6KS7<38>2C12C11B1\ <3>0A00A00B0<4>1C01C01C0<2>1D02E11F11F00F0<13>9Q2AR2AS2<2>CU\ 3DV3FW3<2>K_5L`5M`5<3>Sd6Ue7Vg8<8>iqC } I4KLN12 { ; . t= 0:10:02.87 ; Copyright Sylvie Gallet, Jun 04, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=1.71969/-2.35288/1.504424/1/37.4999999999997442/2\ .58335020042466112e-014 params=3.32/4/0/0.6 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=zzz<93>444333222<2>000000111<10>CCCDDDEEE<13>NNNOOOPP\ P<69>sssssssssssssss<41>yyyyyyyyy<3>zzz```CCC222 } I4KLN13 { ; . t= 0:04:53.19 ; Copyright Sylvie Gallet, Jun 04, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-1.67651/-2.6917/1.467893/1/-75.0000000000000995/\ -1.39561973089286084e-013 params=3.1/4/0/0.5 float=y maxiter=1000 inside=0 proximity=10 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=vxc<3>hoadm``k`<2>PcZ<11>gmlhnmjon<3>orsqsurtvtuwuvxw\ wz<159>222222111111000<46>ddgeeheei<3>iimzzzzzz000000zzzzzz } I4KLN14 { ; . t= 0:08:04.06 ; Copyright Sylvie Gallet, Jun 04, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-0.682655/-1.97762/1.505438/1/-42.500000000000142\ 1/-7.59461937782646146e-014 params=3.12/3.8/0/0.5 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=000<81>RRrSSsSSt<2>TTvUUwTTu<10>HARG9OF7M<3>A0A<13>jS\ 3lU3oW2<3>zc0<17>mP0lO0lN0<2>iK0hK0fJ0dI0<11>L60J50H40<2>C10\ A00A00<74>100100100<3>000cccnnnzzz } I4KLN15 { ; . t= 0:05:24.67 ; Copyright Sylvie Gallet, Jun 04, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-0.639835/-2.16756/2.519123/1/-70/1.3107570584480\ 7544e-014 params=3.12/4.05/0/0.51 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=1/253 sound=off colors=000<105>000000000<3>000wc0<7>WI0SF0PC0<3>A00<9>400400\ 300<3>000UUw<24>E6KE5JD4H<3>A0AE5IC3EA0A<6>60A50A50A<3>20A80\ 0<54>100100100<3>000nnnzzz } I4KLN16 { ; . t= 0:09:26.12 ; Copyright Sylvie Gallet, Jun 04, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=inv4klein_group passes=1 center-mag=-8.31486/-10.129/0.09108612/1/-140/1.310757058448\ 07544e-014 params=3.1/3.1/0/0.8 float=y maxiter=1000 inside=0 proximity=4.6 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=000<182>000000000000000<10>0A00B00C00D00E0<2>2G03H05I\ 0<3>AM0BN0CO0DP0<10>_fDahFciGekHgmIjoK<3>ptSruUruV<8>txitxju\ xl<3>vzs000<2>000 } 4akln01 { ; . t= 0:01:27.94 ; Copyright Sylvie Gallet, Jun 05, 2002 ; <sylvie_gallet(a)compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=4apolloklein1 passes=1 center-mag=0.0159799/0.027678/1.572327/1/29.9999999999999964\ /-1.23373533611470521e-014 params=-0.5/0.8660253999999999/0.8660253999999999/-0.5/-0.86\ 60253999999999/0.8660253999999999/1/0/0.8660253999999999/0 float=y maxiter=1000 inside=0 proximity=1.5 outside=fmod periodicity=0 cyclerange=0/255 sound=off colors=111<3>000A00<4>J40L50N50<3>V90XA0ZB0<2>bE1cG1dH1fJ1gK\ 1<6>oV1pW1rY1<2>ua1wc0vb0<18>bF0aE0_D0ZC0YA0<26>720620520<3>\ 000A00<39>720720720<2>630630741<2>963963963963963<104>111 } ----------------------------------------------- E-mail: Sylvie_Gallet(a)CompuServe.com Web site: http://www.fractalus.com/sylvie/homepage.htm -----------------------------------------------

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FOTD 03-06-02 (Cubic Mandelbrot [6])
by Jim Muth 03 Jun '02

03 Jun '02

FOTD -- June 03, 2002 (Rating 6) Fractal visionaries and enthusiasts: Things are moving on schedule here at fractal headquarters, which means that the CD is entering the late mid-stage, the ongoing fractals are continuing to appear, the cats are sleeping, but I have yet to receive the 24-million dollars I was promised by that man who sent me the e-mail. :-) Today we take a trip to the cubic Mandelbrot set to see a cubic midget. The cubic set is basically an extension of the classic quadratic set M-set, with corresponding features in corresponding areas. The main difference is that there are 2 lobes in the buds, and instead of the 2,4,8... arrangement of elements around the midgets, the arrangement is 3,9,27... It also becomes meaningless in the cubic set to orient midgets in the 'normal' manner, as I do with quadratic midgets, since cubic midgets have 4-way symmetry. I have given today's midget a diagonal orientation, which is both dynamic and somewhat artistic. As is the case with most of the FOTD's, the coloring is done with the standard equal- iteration-band method, with the inside set to black. Feeling that the image has at least a modicum of worth, I rated it at a 6. The name "Cubic Mandelbrot" is a description of the image, with no pretense at cleverness. The 11-minute render time makes running the parameter file a drag. The wiser choice is to let Paul and Scott do the dragging, and download the completed image from their web sites. Paul's site can be found 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 Sunday here at Fractal Central was near perfect, with total sunshine and reasonably happy cats. The slightly too-warm temperature of 88F 31C was offset by low humidity and a fresh breeze. The cats would rather have had no wind, because wind conceals the presence of intruders. But they took the breezes in stride and explored the yard peacefully. Being faced with a day of work, I must now end this latest chapter in the unending series of FOTD's, but I'll return on schedule on the next day evenly divisible by 3 -- June 6. Until then, take care, and search for the meaning in fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Cubic_Mandelbrot { ; time=0:11:06.68--SF5 on a P200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotCube passes=1 center-mag=-0.00037280362079087/+1.091145090358868\ 00/1.05861e+010/1/-19.9998811849355604/-0.00012469\ 0785224791656 params=0/0/0/0 float=y maxiter=6000 inside=0 logmap=836 periodicity=10 colors=000Skz_mzhozspzqqzqrzqtzqtzqtzqszqrzqqzppzp\ ozpnzpmzplzpkzpjzpizphzngznhznhznhznizniznjznlznkz\ mlzmkzmkzmkzmizmizmhzmhzmhzhgzegzbgu_enXehUe`PcWMc\ OJcIGbCEb5Bb06`08b08b08b08b08b18b29b59c69c89cB9cC9\ cEBcFBcIBeJBeLBeOBePCeRCeUCeWCgXCgZCg`EgbEgcEggEgh\ EhiEhmFhnFhpFhqFhuFhvFiwGizGizGizGizGizGizGizZX0XW\ 0XW0WW0WW0WW0UW0UW0UW1SW4SW5RW6RW8RW9PWBPWCPWEOWGO\ WIMWJMWLMWMLWOLWPJUPLWRMWSMXUOXWOXXPZZPZ_RZ_S_`S_b\ U`cU`eW`gWbhXbi__hXbiWekUhmSimRmnOppMsqLuqJwsIzuFz\ vEzvCzwBzy9zyBzvCzsCzpEzmEyiFvgGscGp`InZIkWJhSLePL\ bMM`JMZGOWEPRBPO8RJ5RF2SB0S90W80X80Z90_90`91bB1c92\ e92gB4hB4iB5kC5mB6nB6pC8qC8sC8uC9vC9wBByBBzBCzBEzB\ GzBJz9Mz9Pz9Sz9Wz9Zz9`z9czGgzMizSmzZpzeszkvzqwzwyz\ uzzszzqzznzzmzykzwhzugzsezqczpczmczkcziczhczeczccz\ bcz`czZczXczWczPczUczXcz_czcczgczgczgczgczgczgczgc\ zgczgczgczgczgczgczgczgcz } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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