- Fractint - mailman.xmission.com

FOTD 16-01-03 (Negative is Positive [4])
by Jim Muth 16 Jan '03

16 Jan '03

FOTD -- January 16, 2003 (Rating 4) Fractal visionaries and enthusiasts: I am always fascinated by polytopes of higher dimensions, particularly the regular polytopes of the fourth dimension. In 4-space, six regular polytopes exist. The 5-cell corresponds to the tetrahedron of 3-space; the 8-cell, to the cube; the 16-cell, to the octahedron; the 120 cell, to the dodecahedron; and the 600-cell, to the icosahedron. But in 4-space there also exists a polytope known as the 24-cell, which would appear to have no corresponding figure in 3-space. This appearance is not totally true. The 24-cell has no corresponding regular figure in 3-space, but it does have a similarly constructed figure -- the rhombic dodecahedron, which consists of 12 rhombic faces, 24 edges and 14 vertices. Curiously, the rhombic dodecahedron is a space-filling figure. In tomorrow's discussion, we shall construct a 24-cell polytope from the ground up, but before then, we have today's fractal to examine. Today's image is named "Negative is Positive". I gave it this name for two reasons -- first: many of my images result from combining negative powers of Z, which is a positive thing, and second: I received a junk e-mail this morning from a spammer, which is nothing unusual. But this letter was intended to sell an anti-spam program to me. It began by saying "If you had our product, you would not have received this letter." My mental reply was, "It's always best to start the day with a laugh." Then, after a moment's consideration, I deleted the e-mail and named today's image. Though its name was given in jest, today's image has perhaps a bit more of the negative than the positive about it. The rating of 4 is quite a comedown from yesterday's, but then, we can't be above average on every day. And yes, the image was created by combining two negative powers of Z, in this case -3 and -5. The parent of today's scene is a rather comical figure resembling a lobster sitting on its blunted tail. Today's image is located at the tip of an irregular filament near the point where the lobster's right claw joins its body. The image renders from the attached parameter file in just over 3 minutes. The GIF file of the completed image downloads in even less time. The download may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With a temperature of 25F -4C, Wednesday was very cold and windy here at F.C. Occasional flurries of snow made things even worse. The F.C. cats spent the entire day indoors, checking the outside conditions several times, but turning around as soon as their sensitive noses felt the chill. Today is starting just as cold, and more snow is threatening. The cats will have another unsatisfactory day. My day will be satisfactory if I find a perfect fractal, which is unlikely. Until next time, take care, and remember that no one is perfect. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ NegativeIsPositive { ; time=0:03:15.26--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.23970545929533/-1.269509193680854/9.\ 148861e+009/1/170/7.41674007990883455e-005 params=1/-3/0.5/-5/0/0 float=y maxiter=1200 inside=0 logmap=60 periodicity=10 colors=000OCVPCYQAaT9gV7jW5iX3n`2qd1ph1nl0mp0kt0ix\ 0hz0fz0ez0dx0ct2aq5`m8_iAYfCYcGX_IWWMVTOTPSSMVQJXQ\ I_PH`PHaPGdOGeOFfODhODjNClNCmNBoNAqMAsM9tM9vMDtLIt\ JNtIStHXtGatFftDltCqtBwtAztAxpBvlCthDqdFo`GmXHjTIh\ PJfMLdIMaFN`BOY8PW5QV2QQ8TNDWJJYHP`DWcAae8ffBhhDhi\ GijIilLjmNjoQloTlpWmqYms`otcoveovcisaep_aoYYlXViVQ\ hTNeSJcPGaOC_N9Y1DD1AG08I05L03M52TB1_H0eN0lT0sS2tQ\ 5tP9tOCvNGvMJvLNwLQwJVwIYxHaxGexFizDmzCqzCvzVpqmjj\ hihdhe`fcXeaTd_OcXLaVHaTD`QA_O5YM2XL0WI0VG0VF0`P0f\ _0li0st0xz1mz8cvFVqMLmTCizpHzoFzmCzmBzl9zl7xj5wj3v\ i1th0sh0qf0pf0oe0oe0WJ5D0LI5MNANSGOXMP`QQeXSjcTpiV\ toVvmNvoGvq9vs3su5pw5my5jz5hz7ez7cz8az8_zAYzCXzDWz\ GVzITzJSzMQzNOzPNzSMzTLzWJzYIz_HzaGzcJzWMzOPzHSzBW\ zLYzV`zcczmezwazq_zlXzhVzcSzYPzVSzWVzWXzW_zXazXdzX\ fzXizYlzYozYqz_tz_wz_zz_xzYxzYxzXxzXwzWwzWwzWwzVwz\ VvzTCz5FzAGzDHzHJzMLzPMzT } 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==================================

1 0

inside=atan
by Guy Marson 16 Jan '03

16 Jan '03

Dear Jonathan, Stone-Soupers, Fractinters, high magnifications of midgets with 'inside=atan' are highly maxiter-sensitive, thus pretty difficult to manage. Is there a trick to find the right value for maxiter? After a time consuming 'try ad error' periode, I found a way to get appropriate maxiter=nnn values. Here are examples for 5 orders of maxiter. Low mag's as 'startman' are easy to manage.. No value for maxiter below the value for the first order leeds to a nice pic and the value for the first order is no easy to find.. So it would be great to implement 'maxiter' to the evolver, and, if it's possible, the 'proximity value for inside=epscross and fmod' (x-screen) too.. Try to change the values for maxiter and see the results.. startman { ; time: 0h15' on a K7/600 ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=d center-mag=-0.538232/0.00782014/0.929296/1/-90/3.88578058618804789e-016 params=0/0 float=y maxiter=8000 inside=atan symmetry=none periodicity=0 cyclerange=1/1 colors=000<3>321421031642<51>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000\ 001<56>Q_tQ`uR`v<2>SbyTczSby<61>000 } ataniter { ; 1th order =12033 ; time: 0h26 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201844790/+0.05435555412152205/7.927134e+011/1/-4.\ 99675937785410795/-0.0902709561915964742 params=0/0 float=y maxiter=12033 inside=atan logmap=yes symmetry=none periodicity=0 colors=00000T<24>005004003<2>000000222<4>DCEFEGIGI<3>QORSQTUSW<4>c`ddaff\ ch<3>lhnmjonkq<3>soutovtpw<3>wrywszwsz<2>xszxszwry<6>sousnurnt<3>okqnjpl\ in<2>hejgciebgc`e<3>XVZWTXURV<5>HGIFEGDCD<3>444<39>ma1na1pb1<2>se1se1re1\ <3>pc0ob0ma0<27>860750540430220000<34>00`00a00b00c00d00f<13>00U } atannumb { ; 2th order =24066 ; time: 1h26 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201845010/+0.05435555412154748/2.119379e+012/0.999\ 9/-4.99548275077093162/-0.086997345982712887 params=0/0 float=y maxiter=24066 inside=atan outside=0 symmetry=none periodicity=0 colors=000000<57>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`\ uR`v<2>SbyTczSby<61>000 } atanfmod { ; 3th order =36099 ; time: 0h46 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201844790/+0.05435555412152205/6.97086e+011/1/-4.9\ 9687607663320321/-0.0914427337369515397 params=0/0 float=y maxiter=36099 inside=atan proximity=0.007 outside=fmod symmetry=none periodicity=0 colors=000000<57>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`\ uR`v<2>SbyTczSby<61>000 } atansumm { ; 4th order =48132 ; time: 0h55 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201844790/+0.05435555412152205/1.113368e+012/1/-4.\ 99670916040466828/-0.0879347820503879468 params=0/0 float=y maxiter=48132 inside=atan outside=summ logmap=yes symmetry=none periodicity=0 colors=000A81<3>431320110000000<29>4hg4ji4kj<3>5qp6sq6ts<3>6zy<30>2IH2GF\ 2FE<3>198077065<2>011000001<34>HNqHOsIPt<2>JRyKRzJRy<34>349237226<2>0010\ 00110<29>hZ7j_7k`7<3>qe8sg8th8<3>zl9<33>C92 } atanatan { ; 5th order =60165 ; time: 1h22 on a K7/600 reset=2002 type=mandel passes=d center-mag=-0.74896255201845010/+0.05435555412154748/1.356392e+012/1/-4.\ 98344032497560363/-0.100894378737287849 params=0/0 float=y maxiter=60165 inside=atan outside=atan symmetry=none periodicity=0 colors=000<58>ARtASuBSv<2>BUyBUzBUy<55>136125024<2>001000110<56>tr9us9vt\ 9<2>ywAzxAywA<61>000 } have fun, Guy

1 0

FOTD 15-01-03 (Nest of Tachyons [8])
by Jim Muth 15 Jan '03

15 Jan '03

FOTD -- January 15, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a lot like yesterday's, though I spent a bit more time on it and worked the coloring up to where the image earns a somewhat liberal 8. When I was finished, I named the image "Nest of Tachyons". Like the name I gave yesterday's FOTD, the name of today's image has little to do with the image's actual appearance. In fact, certain colorations that I tried and then discarded resulted in an image resembling rings of shark's teeth. Tachyons are hypothetical particles that travel faster than light. Perhaps it would be best to call such particles imaginary, for there is no evidence that they do exist and good reasons why they cannot exist. But if such particles did exist, they would travel backward in time. They would reach their destination before they left their point of departure. This attribute of tachyons might raise thoughts of backward time travel. We might latch on to a tachyon and go back in time to warn our earlier selves of all the mistakes we have made. If we could go back in time only a few hours, we could give ourselves the winning lottery numbers in time to buy a winning ticket. It's a good dream, but it will never happen. The natural world seems to treat backward travel in time as a taboo. Every time we discover a way we might do it, we soon find a reason why the way we have discovered will not work. No matter how clever our schemes, we are frustrated by some ineluctable law of nature. It reminds me of the situation we face with the uncertainty principle. If we try to determine both the position and momentum of an electron at the same time, we find the task impossible. The more accurately we know one, the vaguer the other becomes. Something always gets in our way. In this case, it is our assumption of the nature of the unmeasured electron that has led us to mistakenly look for something that does not exist. An electron is a wave of probability, with no definite attributes until we pin it down by our measurement. We naturally cannot measure what does not exist. I strongly suspect that when we contemplate the possibility of backward time travel, we make another wrong assumption. We assume time itself to be something that it is not. That 'grandfather' paradox could be trying to tell us something important. We often see black holes presented as possible means of time travel and faster-than-light travel. The problem with this method is that we could not survive the tidal forces as we pass the singularity. We also see multiple universes optimistically mentioned as a possible means of going backward in time. We have dark matter and dark energy which some say could be the gravity of these alternate worlds bleeding into our own universe. We have a cosmic repulsive force, which is said to result from the energy of the vacuum. We have many signs and theories that other worlds might exist, but no possible way of reaching them. We must face the fact that our one-way trip into the future, which actually is time travel, cannot be escaped. And I must face the fact that I have again wandered from the topic of fractals. I can see no way in which fractals could be a means of time travel, but stranger things have happened. With its 5-minute render time, today's image is mercifully fast. But even faster is the download 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> It was quite cold here at Fractal Central Tuesday, remaining just below freezing despite the strong sun. At this time of year the earth is about as close to the sun as it ever comes, yet the temperature is about as cold as it ever gets. Not concerned with astronomical trivialities, the dynamic ones (cats, that is) remained outside only a few minutes before getting their whiskers chilled and retiring indoors to their favorite heat sources. Today is starting cold again, and to make things worse, a fresh dusting of snow is on the ground. The fractal cats will not want to hear this. As for me, I always take whatever comes. (I have no other choice.) Until next time, take care, and never forget that we are made of tardyons. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Nest_of_Tachyons { ; time=0:05:43.17--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.36800428773697500/+0.557337704952596\ 80/2.390289e+007/1/-37.5/-6.94211269788858054e-008 params=3.7/-0.85/0.1/-8.5/0/1e+100 float=y maxiter=120 inside=fmod proximity=0.5 periodicity=9 colors=0005zA5zA8zD8zD8zGAzGAzGAzIDzIDzLGzLGzOGzOI\ zOIzQIzQLzTLzTLzTOzWOzWQzYQzYQz_Uz_Uz_UzbWzbWzeWze\ YzgYzg`zg`zj`zjczmczmczoezoezoezrgzrgztjztjzvjzvmz\ vmzymzyozzozzmzzozzozzozzozyozyozyozyozvozvozvozto\ ztoztoztozrozrozrozrozoozoozoozmozmozmozmozjozjozj\ ozjozgozgozgozeozerzerzerzbrzbrzbrz_rz_rz_rz_wzYwz\ YwzYwzYwzWwzWwzWwzTwzTwzTwyTwyQwyQwyQwxQxxOyxOzxOz\ xLzxLzxLzxLzxIzxIzwIzwGzwIzxIzxLzxLzxOzxOyyQxyQwyT\ wyTwyWvzWuzYtzYsz_rzbqz_pz_oz_nz_mz_kz_iz_gz_ez_cz\ _az__zYYwYWwYUuYPuYKrYFpYApY5nY2kY2kY2hW2hW2fW2cW2\ bW2aW2`W2_W2YW2WW2UW2SV2RU2QT2PS2OR2NQ5MP5LO5KN5JM\ 5IL5HK5GJ5FI5EH5DG5CF5BE5AD59C58B57A56A55A54A53A82\ A81A80A80A80A80A80A80A80A80A80A80L80L80L80L80L80L8\ 0L80L80LA0OA0OA0QA0QA0TA0TA0WA0WA0YA0YA3_A8_ABaAGc\ AIeAKgAMiAOkAQmASoAUqAWsAYuA_wAaxAcyAezAgzAizAkzAm\ z8oz0qz0sz0uz0wz2xz2yz5zz } 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==================================

2 2

FOTD 14-01-03 (Polytope Paradise [6])
by Jim Muth 14 Jan '03

14 Jan '03

FOTD -- January 14, 2003 (Rating 6) Fractal visionaries and enthusiasts: While at least one member of the Fractint list appears to perhaps be losing a bit of enthusiasm for fractals, there is no danger of a similar fate befalling myself. The only thing I regret is that I lack the time to explore more of the infinitely infinite world of fractals. Perhaps the first sign of impending boredom with fractals is the desire to add multiple layers, as if a single-layer fractal needed something to give it more interest. Then again, perhaps my devotion to single-layer fractals is an individual quirk of mine, caused perhaps by my typical male tendency to concentrate on one task at a time. After all, multiple layers works very well in the case of music, which is candy for the ears; why not in the case of fractals, which are candy for the eyes? I named today's image "Polytope Paradise". I can give no logical reason why I chose such a name, since a polytope is a geometrical figure, existing in n-dimensional space and enclosed by a finite number of planes or hyperplanes. The strings of bubbles in today's image are enclosed by curved 2-D surfaces rather than planes, and therefore cannot truthfully be consid- ered polytopes. As a matter of interest, the word 'polytope' was invented by Alicia Boole, the daughter of logician George Boole. In 1-space and 2-space, an infinity of regular polytopes are possible. In our everyday 3-space, only 5 regular polytopes are possible. In 4-space, 6 are possible, but in 5-space and all higher spaces, only 3 regular polytopes can exist. Today's image is another ghostly one, consisting entirely of trapped points whose orbits have been made visible by the bof60 inside fill. The generating formula combines 1/Z and Z^(-2), then adds 1/C. The image itself rates a 6. The render time of 41 minutes for today's image is admittedly slow. The wait can be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was actually not too bad on Monday, with warm sun, little wind, and a temperature of 43F 6C. The fractal cats found the outdoors reasonably comfortable. Tippy, the lean lanky tabby, spent nearly two hours in the yard. Thomas, the overweight yellow, returned indoors after one hour. No treats were needed. Today however is much colder, and the dynamic pair will not find it so pleasant out of doors. I will not find it pleasant until the work is finished. The next FOTD will appear in 24 hours, so take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Polytope_Paradise { ; time=0:41:12.86--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.84049791931695570/+0.257654873112327\ 50/235620.6/1/-65/5.48976843151027794e-010 params=1/-1/1/-2/-32/1e+100 float=y maxiter=900 inside=bof60 logmap=yes periodicity=10 colors=000zzzzwyzuxzswyqvyouymtxlsxksxjrwirwhqwgqv\ fpqepldjgbcb`YYZRTXLNWGOVFPUFPTEQSEQRERQDRPDSODTNC\ TMCULBUKBVJBVIAWHAXH7YGAZFD_FF`EIaELbDNcCQeCTfBVhB\ YiA`i9bhAbgAaeA_cAZaAY_AWXAVUAUSBSPBRNBPLBOJBNGBME\ BKD8KCBJBDI000AIHALG9NG8PF8SE7UE7XD6ZD6aC5cB4eB4hA\ 3j93m92o82q84o96mA7kB9jCAhDCfDEeEFcFHaGI_HKZHMXINV\ JPUKQSLSQMUPMVNNXLOYJP_IQaGQbERdDSeBTg9Uj6Vh8Ug9Uf\ BUeCUdEUcFUbHUaIU`KUZLUYNUXOUWQUVRUUSTTUTSVTRXTPYT\ O_TN`TMbTLcTKeTJfTIhTHiTIqNGjTEcZCXdAQj8Jp5Dx7Cv9C\ uACtCBsEBrFBqHBpJAoKAnMAmNAlMBkMBkMCkLCkLCkLDjLDjK\ EjKEjKEjKFiJFiJGiJGiJGiIHhIHhIIhHIhHIhHJgHJgGKgGKg\ GKgGLfFLfFMfFMfFMfENdEOcDPbDQ`CR_CSZCSYBTWBUVAVUAW\ T9XR9XQ9YP8ZO8_M7`L7aK7aJ6bH6cG5dF5eE4fC4fB4gA3h93\ i72j62k50m22k44j66i88g99fBBeDDcEFbGGaII`JKZLMYNOXO\ PVQRUSTTTVSVWQXYPY_O_aMacLbdKdfJfhHgjGikFkmDloCnqB\ prAqVNIXPLYQN_RP`SRaTTcUV } 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==================================

2 1

FOTD 13-01-03 (Mysterious Energies [7])
by Jim Muth 13 Jan '03

13 Jan '03

FOTD -- January 13, 2003 (Rating 7) Fractal visionaries and enthusiasts: Unable to find a good opening for today's FOTD discussion, I shall simply place my mind in idle and let my thoughts ramble where they will. Now let me see . . . Every day for almost the entire life of the FOTD, I have opened the discussion with the line 'Fractal visionaries and enthu- siasts'. I do it without thought of the meaning, since the line is part of my pre-formatted FOTD template file, and is inserted into the text of the discussion automatically. The nature of the fractal enthusiast mentioned in the line is obvious, but what is a fractal visionary? My dictionary defines the word 'visionary' both as an adjective meaning 'existing only in the mind', and as a noun meaning 'a person who sees visions of hidden things'. So a fractal visionary is one who sees visions of the normally hidden things known as fractals, (which BTW are only partly unreal). Those who can see things, real or unreal, that others cannot see are also known as mystics. In times past, mystics were seen as wise people; in our present age of reason run amok, they are looked upon as a little weird, amusing but harmless -- that is unless they start claiming and convincing too many others that their visions are actual glimpses of other real worlds, in which case they must be shown to be deluded. In this age of reason, there is and can be only one real world, the physical world, with which we can be in touch. There is no possibility of interaction with other real worlds, which preferably do not exist. This status quo must be preserved at all costs. Well, I often see things that others cannot see with eyes alone, though I'm not sure if this makes me a mystic. The things I see are called fractals, and must be seen with the aid of a computer and monitor. With my real eyes, I can see fractals on my computer screen whenever I wish, and I sometimes see them in my dreams as real 3-D objects existing and evolving in 3-D space. Since others can at least see my fractal visions on their own computer screens, I guess this makes me a mystic of the second order. I could not be a mystic of the first order unless others could also see the fractals I sometimes dream of in my dreams. Today's image is a fractal of the third order. It is mystical in the sense that it cannot be seen without the aid of a computer and also that it is another of my 'evaporated' images, which consist entirely of the ghost of a fractal that once was there. (To see the fractal that once was there but has vanished, change the imag(p3) parameter from 10^100 to zero.) The parent of today's image consists of a multi-lobed string of bays extending north to south. A filament extends southwest from the southernmost bud, and terminates in a zig-zagging ring. Today's scene lies on this ring, not far from where the filament joins it. I named the image "Mysterious Energies" for no good reason, and rated it a 7 because in my opinion it is above FOTD average. The render time of 9 minutes is a bit beyond the range of reason for those with busy lives to lead. But the already completed GIF image is available for download on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday was sunny but cold here at Fractal Central, with a high temperature of 29F -1.5C. The cats endured their indoor confinement with patience, blaming me only twice for the chilly conditions beyond the door. Today has so far been uneventful. Hopefully, it will remain so, as there is a bit more than the average amount of work to be done. Until next time, take care, and is it reasonable to believe that fractals are real? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MysteriousEnergies { ; time=0:09:16.89--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.80567324593928600/-2.034640713112640\ 00/2.056237e+009/1/-62.5/2.93630749607157182e-005 params=-7.57/-1.5/-0.98/-6.5/0/1e+100 float=y maxiter=900 inside=bof61 periodicity=10 colors=000_QjXSl000STmVXgXYaY`Y_aS`dOcfIdiDfj7gm3i\ o0jp0fo0co4`oAYmFVmLSmQOlXLl`IlfFjlCjr9jvDdxI`xMVx\ QQyVLyYGyX`pXuiXzarz0mz0jz0gy0dv0as0_p0Xm0Tj0Pg0Md\ 0Ja0000DX0AT07Q04P0CV9J`GQdOYjVcoaczfczigzclm_o`Ts\ OPxAJz0Fv1Js4Mp7PmASjDVgGYcJ``McYPfVSiSVlPYoGMv9Cz\ 11z00z0Az0Tz0jzLVTfG0cM0aS0`X1Ya4Xg6Vl7SrA000PzDQz\ GSzITzLVzMXzOYzQ_zS`zTazXczYdz_fzagzcizdgxc000dpac\ m`ci`000`aY__YYVXYSX`VQaXLc_Fd`Agc4id0jg0li0gf0dc0\ ``0YY0TV0QS0MP0JM0FJ0CG07D04A00700410A10730N40F40P\ 60L60S70S70Y90_A0eA0dC0nC0lD0uD4iAGi9T_7dV4rP3zL1y\ Q6uV9r`CmdGiiJfoMasPYxTVzXQz_OzaPzcQzdSzfSzfTzgVzi\ XxiXvjYul_rl`pm`oo00ocjpdirdgrQfpCfo0fo3_f6T_0S_0S\ _0Ma6Gd_QT`Qa`QjgJ`mCQu4Gz07x4MvA_sGlrMypSzmXzl`zj\ dziiz90_DAPIQGMg6Px0Ts1Yo6aj9fgDjcGo_LsXOpTGmQAfMG\ _IMSDSM9YF4c70i10m41f66_7AT9FMAJGCO9DS37`01g0Ai0Ij\ 3Pl7XmCcoGjpLrrPyrTupQpoP } 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==================================

1 0

FOTD 12-01-03 (Hidden Flames [5])
by Jim Muth 12 Jan '03

12 Jan '03

FOTD -- January 12, 2003 (Rating 5) Fractal visionaries and enthusiasts: I'll have to keep today's discussion short. It's already past 10am and the Fractal Central support staff is becoming impatient to set out on a trip to search for some old and worn-out objects which she must have. When the parameters of today's image are entered into the MandelbrotMix4 formula, all the excitement lies beyond the right edge of the default image, where a pair of siamese minibrots straddles the X-axis. Today's image lies in a spiral in the shoreline chaos of the bay that connects the pair. I named the image "Hidden Flames" because of the subtle flame- like features that dot the arms swirling toward the center. I rated it at a 5 because, despite my best intentions, it is still only an average image. A bit farther out in this same area lies a row of minibrots unlike any I have seen before. If things work out well, these midgets in a row may appear in a soon-to-come FOTD. The 14-minute render time drags when the fractalist has other things to do. It would be more convenient for most to download the already-rendered image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though we had brilliant sun all day Saturday, it was quite cold here at Fractal Central, home of the dynamic duo of fractal cats. Brisk winds and a temperature in the 20's F, minus single digits C, kept the dynamic ones indoors, behaving very un-dynam- ically. Since cats of the fractal variety need outdoor warmth to enjoy life, the cats were unhappy, and a treat of tuna only partly lifted their flagging spirits. Today is once again cold, but not quite as cold as yesterday. Maybe the duo can find peace of mind. As for me, I find I have semi-volunteered for a trip to a local antique mall. These 'shopping' trips always raise the question, "if you don't know what you're shopping for, how will you know when you find it?" Until tomorrow, take care and keep your cat warm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hidden_Flames { ; time=0:14:24.46--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.85671879185512400/+0.016441220570067\ 03/7117130/1/85/7.17137860692385054e-008 params=4/-6.4/-6/-3/0/525 float=y maxiter=12000 inside=0 logmap=220 periodicity=10 colors=000CzzCxz5wz7uz7tx7ru7qr8oq8nn8nk8lh8ke9ic9\ h`9fZ9fa5hS9cVCbWE`ZIZ_LXbNVcSTfVQhXPm`Ml`JoiLybIn\ eGsbDlbAr`8i_7hZ4eK0KW0aV0_T0ZP0`S0XV0TX0Q_0Mb0Je2\ Gh3Dk59n75q93tA0wD0zE0zC0zG0zJ0zN0zS0zW2z_5zc8zhCz\ lEzqHzuLzzNtzQezWoz`0ziize2zb7z_AzWGzTJzQNzNTzJXzH\ bzEfzAlz8qz5xz0uz3tr4rk5ob7nV8tM8lN9fPA`QCWQDPSEJT\ GEVH8XJ9VHATECSCDQAEP8GM5HQ3IJ2JW0LH0M_0IT8GfLCuZ9\ l_Ew_IePN_ESV4P55NP7M88J99IAAHCCEGEGDDHCCI9CJ8AL5A\ M49N29N08P08Q07S07T05V05W04W04Z08`0Ac2Df5HiAJlEMoJ\ QrNTuTWxXZwZWu_TpTQtTNtcLreIreGqfDohAoi8nk5nl3ln0l\ n0if5h`CfWIeQNcLV`G`_AfZ5nX0uW0z_2zb7zfCziIzlNzqTx\ t_xxbxzbxzbxzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzb\ zzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzczzczzezzezzfzzfzz\ hzzhzzizzizzkzzkzzlzzlzznzznzzozzozzqzzqzzqzzqzzqz\ zqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzqzzq\ zzqzzqzzqzzqzzqzzqzzqzzqz } 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==================================

1 0

FOTD 11-01-03 (Down Down Down [5])
by Jim Muth 11 Jan '03

11 Jan '03

FOTD -- January 11, 2003 (Rating 5) Fractal visionaries and enthusiasts: For today's FOTD fractal I simply changed the 2's of yesterday's formula to 3's. Some adjusting of real(p3) was necessary to produce a promising fractal. The fractal that resulted is an oversized circle filled with debris. Today's scene is located at the bottom edge of this bloated circle. I named the image "Down Down Down" because while studying it for a name, I had the impression of looking down at the burning coals of a fiery pit, maybe not the pit ruled by Hades, god of the underworld, but fiery nonetheless. The image has little going for it other than the effect of a bed of glowing coals toward the center, thus I could rate it no higher than a 5. But, rendering as it does in less than 2 minutes, the image at least will consume little of the time of those who choose to run the parameter file. As always, the completed GIF image is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Friday weather was typical of the season here at Fractal Central, with clouds, sun, wind, flurries of snow, and a high temperature of 38F 3C. Despite the chill, the fractal cats managed over an hour in the outdoors. When they came in, they were both happy and hungry. I have a relatively slow day ahead of me, which should give time for an above average fractal for tomorrow. Until then, take care, and I've found a projective plane, but it's too large to fit on the shelf beside my Klein bottle. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Down_Down_Down { ; time=0:01:55.34--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.07563752269483708/-7.541266062129865\ 00/5.6606e+009/1/-102.5/-0.0246641156100383535 params=3/3.3/-3/-3.33/-0.995/0 float=y maxiter=350 inside=0 logmap=36 periodicity=10 colors=000IHzBSz4Xz0iz2jz9dwEZoKTgQN`SHOaBLj9Bm72r\ 50z40zZ0zc4zhDznAWB7VA5R92Q71Y9AdAIlBRrDZzEgzGpzHx\ zO`rWElNOeGZ`9iV1tO0zL1lI7VGDDDI0Lz0QxATwLWuW`tgcr\ tepzGNm00Z07d5IiEVmLetVrxazzRzoHzc9xR0wG0u40l5Ad5K\ W5TO5aaDjmItzQzzWwzZtz`pzcmwdjrggoidgcaaY`WTYONVIH\ TDDWIGZOIaVLc`OeeRilVjpYelQagIZcDV`5RW0NR0KO0HWAGc\ YEjuGYiGLZG9NG0DzVIzLGmDE`4BN0AZ7EjGHwOKoVLiZLadNW\ iNOoOItOLxZNzgOzpTzeYwWatNepDim4dd9aWBZNGVEIR5NO0Q\ K0KG0EB097022002cr9YoDTlINjNIgTDdY9cc2`g0Zi9ZiIZiT\ ZicZimZ`cLRTAII0A90EB1IDHNEYQGlWHdaIYgKQlGWoDarAew\ 7lz4rz1wxKrtcoowjlzgezi`rjVelOWmIKoDAp70r`RdTKgLEj\ E9m72p2Hj0Wd0i`0xV0zQ0zK0zE2zA7z4Bz0Ez0Iz0Lz0Qz0Vz\ 7ZzHazTezdjzoozzrzzozZmz0iz9dzHazRYz`VziRzaQzVOzNN\ zGLz9Kz1Rz9ZzEezKmzRuzYzzczzizzrzzzzzzzzzzzzzzzzzz\ zzzwzzuzzKz0Hz0Ez0Dz0Gz0Iz0Lz0Oz0Rz0Tz0Wz0Zz0az0dz\ 0ez0az0Zz1WzARzIOzRLz`Qzz } 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==================================

1 0

FOTD 10-01-03 (Two Satellites [7])
by Jim Muth 10 Jan '03

10 Jan '03

FOTD -- January 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: To produce today's fractal, I took most of the 1's in the formula of yesterday's fractal and changed them to 2's. I had no mathematical reason for doing this, I did it only for fun. (I could not simply change the 1's in yesterday's real(p3) parameter to 2's because doing so would have produced an inferior fractal.) When all the number-changing was finished, I had created another oversized area of chaos, this one with its main Mandeloid well beyond the borders of the default screen. This Mandeloid resem- bles a nearly perfect M-set. Today's scene is located in one of the rays radiating from a larger midget, which lies just beyond the tip of the main stem of the large Mandeloid. Thanks mostly to the strong coloring, the image rates a 7. I named the image "Two Satellites" when I noticed the two prominent areas in the corners of the image, which obviously hold still smaller midgets that are beyond resolution. The render time of 7 minutes is fast enough, but downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will leave more time for other things. Thursday was an exceptional day here at Fractal Central. How often does a day come in the middle of winter, with almost hot sunshine and a temperature of 63F 17C? . . . Once every two or three years? The dynamic cats took advantage of the unusual conditions by spending almost the entire afternoon in the yard, trying to ignore the remaining puddles and mud. Needless to say, their moods were as exceptional as the weather. Today is starting sunny but colder. It will be harder for the dynamic ones to stay happy, but they are already eager to get outside and give it a try. And as always, I have a few tasks to finish, so until next FOTD, take care, and I wonder where I could find a Klein bottle. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Two_Satellites { ; time=0:07:21.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-7.38358917092518/+20.54585830913693/6.\ 4431e+009/1/-122.5/-0.00244863563439755294 params=2/2.2/-2/-2.22/-1.3/0 float=y maxiter=1200 inside=0 logmap=157 periodicity=10 colors=000D9AC0FA3L99P7FT6L_4Qc3Vg1`l0fr0lv0rz0vz0\ rx0mp0ji1fc3aX4_P6VI7SC6I7474301A34I66P97XC9cFAjJC\ rMDyPFzSGzVIzcAzi4zo0vs0sz0ry0rr0rm0rl0pj0pi0pg0pf\ 0pd0oc0oa0o`0r_0uY0xX1xT0xQ0pO0iL0`I0TF0M70OA0PF0Q\ L4SP9TVFV_JXdOYiT_oY`scaygczmdzrdzv_zuTzuPxsJrsFms\ 9gr3ar0Yp0Sp0Op0Jr3Gr9DrGArM7rT4r`1rf0rm0rs0rl0gd0\ YY0PQ0FJ16C30440A60G60L60Q60X60`60f60l60p60v60z60z\ 60y40s30m16g0Ca0GX0MQ0SL0YF0aM0cS0dY1fc4gi7io9juCl\ zFmzGmxPjpYgifd`maTv_MzXFzVVzTizSyuQzoPmpFPr40s04v\ 07x3Ay6Dz9GzCLzFOzIQzLTzOXzQ_zTXy_VldS`jQOpOCvM0zL\ 0zM0zMAvMMpMYlMifMuaPs`Ss_TsYXsXYsV`rVarTdrSfrQirP\ jrPrdaxSozFzz3zz1zz0zz0zz0zz0xz0ux0pv0mu0js0fr0cp0\ `o0Yg6daMlXasTfpSimPmjOpiMrmMusMxxMyzQxsTvjXuc_sVa\ rOcmPciPddPd`PdXPfSPi1zm0zr0zv0zz0zy0zx1zv6zuAzsFz\ rJzpMzoQzmVzl_yjcxigvijvjmpjpjlsflv`lxXmzQmzLozG9z\ LAzICzFDzAFz7Gz4Iz1Jz0Gz4 } 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==================================

1 0

FOTD 09-01-03 (Curlers [8])
by Jim Muth 09 Jan '03

09 Jan '03

FOTD -- January 09, 2003 (Rating 8) Fractal visionaries and enthusiasts: Sometimes I enter parameters into the M-Mix4 formula without thinking, simply letting my fingers go where they may. In today's case my fingers became stuck once again on the '1' key, and tapped out a fractal filled with interesting places to explore. The parent fractal is a hugely bloated crescent-shaped thing filled with chaos, which can be seen in its entirety only after several out-zooms have been made. But despite the overall chaos, a relatively small area of smooth circular bands lies near the origin, with a Mandeloid just to the north. The smooth bands and chaos come together in the East Valley of this Mandeloid, forming the most interesting area of the entire fractal. Today's scene lies in this East Valley, where the smoothness begins breaking down into chaos. I have named the image "Curlers". (Have I used this name before?) The curly things filling the image remind me of those fantastic creatures that appear in certain of Escher's pictures. These curious creatures can curl themselves into balls and quickly roll to wherever they want to go in the impossible worlds conjured up by Escher's imagination. I rated the image at a much-above-average 8. The average in this case is the average worth of the typical hastily constructed FOTD image, not those carefully-crafted images that fractal artists have spent weeks or months in creating. The average FOTD image, by its nature, is a quickie. I rarely spend more than 1 to 2 hours on the entire task of finding and rendering the image, and composing the discussion. Today's image renders in 8 minutes. This is fast enough for those who prefer to render their own images, and slow enough to make the download the more efficient choice. The download may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was actually quite pleasant here at Fractal Central on Wednesday, as a chinook wind from the west raised the temperature to 48F 9C and melted the remaining snow, permitting the dynamic duo a brief romp in the yard, if sitting and looking around can be considered romping that is. Today will be even warmer, but before I can even think of the pleasant day outdoors, I must get some work finished. So until next time, take care, and whatever is a chinook? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Curlers { ; time=0:08:05.82--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.64012469245893500/+1.044967891978891\ 00/6.066313e+007/1/-130/-3.89582091792489704e-005 params=1/1.1/-1/-1.11/-0.11/0 float=y maxiter=1100 inside=0 logmap=155 periodicity=10 colors=000H0OI0eJ0dK0cL0bM0aN0`O0_O2ZP3YP4XP5WQ5VQ\ 6UQ7TQ7SR8QR9ORAMSAKSBISCGSCFWHEZLEbPDeTDhXCl`CodB\ shBvlAypAwl9vh8ud8t`7sY7rU6qQ6pM5oI4nF4mB3l73k32j0\ 2g48e8DbCJ`GOYKUWOZTSdRWiP_nQblRekShiTkhUnfVqeWtcX\ wbXyaWrcWkeWdgWYiWRkUThTVeRXbQZ`O`YNaVLcSKeQJgNHiK\ GjHElFDnCBp9Ar69s4IrVRrtVonZmibkdfhZjfUndPraJv_EzY\ 9sUFlQKeMPZIUSE_LAdE6i82nG9bNGRUNF`T4YV7WWAUXCRYFP\ ZIN_KL`NIbQGcSEdVCeY9f_7gb5he3ig9dfF`fLXeRTeXPdbLd\ hHcmDcnHboLbpPaqTaqXar``sc`tg_tk_uo_vsZwwZwzZorXhj\ W`bUUVTMNRFFQKHROJRSLSXNS`PTdRThTTiURiUQiVOiVNiVLj\ WKjWIjWHjXGjXEkYDkYBkYAkZ8kZ7kZ6jXAiVDhTGgRJfPMfOP\ eMSdKVcIZbGabFdaDg`Bj_9mZ7pZ6saBtcFtfJthNujRumWuo_\ uqcvtgvvkvxovsnrnnojnleni`neXnbSm_OmXJmTEmQAmN5mK1\ mH2jH2gH2dH2aH2ZH2WH2TH2QH2NH2KH2HH2EH5GK7HMAIPCJR\ EKTHMWJNYLO_OPbQQdSRfTTdTVcUXaUZ`V`ZVbYWdWWfVXhTYR\ 9ZS8_T8`V7aW6bX6`ZBZ_FY`J } 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==================================

2 1

FOTD 08-01-03 (Happenings-II [7])
by Jim Muth 08 Jan '03

08 Jan '03

FOTD -- January 08, 2003 (Rating 7) Fractal visionaries and enthusiasts: It's another very busy day here at F.C. But despite the work, I have found a fractal worthy of being honored by being declared Fractal of the Day -- FOTD for short. For today's image we again try the fractal trick that worked so well yesterday. Probably due to the color palette, the trick does not work so well today, but it still earns its FOTD. Most of what I said about yesterday's image also applies to today's. When I entered today's parameters, my finger became stuck on the '1' key, though the end value of real(p3), which is -2, changes the '1' of real(p1) and real(p2) to -2. I rated the image at a 7, which is above average. I named it "Happenings-II" because it is largely a repeat of yesterday's image. The render time of under 6 minutes may be avoided by downloading the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Despite ample sun, Tuesday was cold and windy here at F.C. With a temperature of 28F -2C and winds of 20mph 30kph, the outdoors held no attraction whatever for the dynamic duo, who passed the day sleeping and eating. Today is starting cloudy and warmer, with enough work to keep me busy until mid-evening at least. But I'll still find time for the Fractal of the Day for 1-9. Until tomorrow, take care, and when a change is needed, make the change. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Happenings-II { ; time=0:05:49.16--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.41337046687929880/-4.168575424427294\ 00/3.249936e+007/1/75/-1.53247584789434343e-006 params=1/-1.1/1/-11.11/-3/1e+100 float=y maxiter=1200 inside=bof61 logmap=yes periodicity=10 colors=0006eQ7dR7dS7cT7bU8bV8aW8aX8`Y9_Z9__9Z`9ZaA\ YbAXcAXdAWeBVeAczAWg9Wh9Xh9Xi8Xj8Xj8Yk7Yl7Ym7Zm6Zn\ 6Zo5_n6Zo6Zo7Zo7Zo8Zo8Zo8Zo9Zo9cpAZpAZpAZpBZpBZpCZ\ pCZpCZpDXmEWjFUhGTeHRbIQ`JOYKNVLLTMKQNINOHLPFIAczQ\ EGUDGZCGbCGgBFkAFp9Fs8Fw7GzPFqAFoBElCEiDDgEDdFDbGC\ _HCXIBVKBSLAA00NNAKN9IP9FQ8CR8AS77T74V65U76U77U77Z\ 78U89T8AT8AX8BT9CT9DT9DZ9ES9000GSAGSAHSAIWBJRBJRBK\ RBLRBMQCMXCNQCOQCPQDPQDQPDRPDSPDSPETPEUPEVOEVOFWOF\ XOFYOFYOFXPGXPGWQHWQHWQIVRIVRJUSJUSJUSKTTKTTLTTLSU\ MSUMRVMRVNRVNQWOQWOQWPPXPPXPOYQOYQOYRNZRNZSNZSM_SM\ _TL`TL`UL`UKaVKaV9bWFaVKaVP`UU`UZ_Td_TiZSnZSsYRyZP\ xYRxYSwXTwXUvXVvWXuWYuWZtV_tV`sVasUcrUdrUeqTfqTgpT\ hpSjoSkoSlnRmnRnnRonQpoQpoPqoPqpOrpNrpNsqMsqMtqLtr\ KurKurJvsJvsIwsHwtHxtGxtGxuIyuJyuKyvLyvMzvNzwOzwPz\ wQzxRzxSzxTzyUzyUzyUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } 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==================================

1 0