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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For some strange reason, today's FOTD is named "Satin Cyclone". I have forgotten the reason why I gave the picture such a name, if indeed there ever was a reason. Sometimes I pull the names for my FOTD images out of thin air, and today's name may be such an arbitrary one. Regardless of where the name came from, today's image is respectable, though the steady decline in FOTD ratings from the 9 of a few days ago continues. But today's rating of 7 is still above average, making today's image marginally worth the effort of waiting 21 minutes for the parameter file to finish. The wait can be reduced to 12 minutes by resetting the periodicity to 10. This makes the effort of running the parameter file a little less marginal. The mathematical formula behind the FOTD image for today is (Z)-0.13Z^(-11)+(1/C), a surprisingly simple expression that does a lot more than one would expect. The parent fractal drawn by today's formula resembles a circular blob interrupted by a concavity on the west edge. Rendering the outer edges of this blob requires the periodicity to be turned off, though a time-saving periodicity setting of 10 seems to make no difference in the appearance of today's image. The inconvenience of running the parameter file can be avoided by downloading the GIF image from the web at the URL: The fractal weather today was mostly cloudy with a temperature of 45F (7C), which was acceptable to the fractal cats, but not ideal. The dynamic duo ventured briefly into the yard, exploring as far as the tangle of wild roses before retreating to the warmth of their radiators. I did a little philosophizing this afternoon, pondering the consequences of demonstrating that the world is indeed nothing but an illusion common to all people. I decided that the consequences would be very few in the way we live our everyday lives, but quite important to our philosophical and religious viewpoints. I'll go into these philosophical consequences in a future FOTD philofractal discussion. If I'm not overwhelmed by work, the day could be tomorrow. As for this evening, I see that the cats have settled, which means it's about time for me to be doing the same. This means shutting down the fractal shoppe and calling it a night. Until next time, take care, and don't fracture your fractal. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Satin_Cyclone { ; time=0:21:47.17 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-6.680805913828656/-8.301745475499704/562\
06.02/1/97.5 params=1/1/-0.13/-11/0/-60 float=y
maxiter=2400 inside=0 logmap=177 periodicity=0
colors=000wbZxdYzeXzfVweUqdSlbSG0NaaQX`QSZONYNIXNCXM\
7VK1UK0SJ0UK<2>0QI0OI1OI3NG5MG7KF9KFCJFEIEGGEIGEKFCN\
ECOCBRBBUBBV99Y89Z78a78d58e47h37i37<3>SOO<3>bMNeMNhK\
NiJMhJMhIMfGM<2>dENdENbCOaBOa9O`9Q`8QZ7QY7RY5RZ4RZ4R\
Y7SZ8T`9VbBXeCYfEZlF`mGapIbqJdtKeuMfxNhzOi<2>zSmzUnz\
UnzVp<3>z`qzaqzbs<3>zhtzitzjt<2>znuzpuzqw<3>zwxzxxzz\
yzyx<3>znwzlwziuzfuzeuzbty`vxYtxVswSsuQsuNqtMqsJqsGp\
qEppBpp8nn5nm3nm1n<3>n0mn0ln0ln0ln0jn0jn0jj0mf0nb3pZ\
7qV9tREuOGwKKxGOyCRz8Vz4Yz0bz0fz0hz3iw5jq7lm9nhCqb9u\
YEnZIi`MbaQYbSRdXOe`KfdIhhFijGjzIlsJmwKnzMuyNpuOlqQh\
zRdiS`eUXaXRYZN<2>XfBXi1Xl7<3>XwOXySYzXZzZ`z`<2>dzbe\
zbfzd<2>jzelzfmzh<3>szjtzjuzlwzlxzmyzp<2>zzhzzezzdzz\
a<2>zzVzzuzzuzzwzzw<16>zz`
}
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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times.
