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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is another quickie. In fact it's the first midget I came upon in my brief 5-minute exploration this evening. The image was found in such haste because I spent most of my fractal-hunting time this afternoon thinking profound philosophical thoughts and replying to the profound philosophical thoughts of others. The formula that drew the image is a whimsical one that was calculated by the M-Mix4 formula, Z^(-1.618)+1.618Z^(-16.*)+(1/C). The midget in the picture is located toward the center of a shallow valley that divides the main bud of the parent fractal. I named the picture "A Midget in Lilac" because of the color scheme, which features pastel green and lilac hues, arranged around the central midget in an unusual pattern filled with circular disks. The parameter file renders in exactly 2 minutes on a P200, plus 2/100ths of an extra second, which will never be noticed. The GIF image file has been posted in all its meager glory to the Usenet group The fractal weather today was perfect, with a deep blue sky, cottonpuff clouds, gentle breeze, low humidity, and a temperature of 80F (27C), which made the fractal cats ecstatic. Too bad it won't last. My philosophical ponderings are once again in high gear, due in part perhaps to the refreshing weather. I have already posted much wisdom to the list today, endured the mockery of the disbelievers, and come back for more. The debate (if it is a debate) is simple -- I claim that something called God most likely does exist, the disbelievers claim that the idea of God is an invention of man. Assuming that the question has a simple yes or no answer, which is not at all certain, one side must be mistaken. But what is the mistake? I can see no error in the logical scientific argument of the disbelievers, and they have yet to point out other than minor technical flaws (IMO) in mine. It seems as though theists and atheists live in two separate worlds, where identical evidence leads inexorably to opposite conclusions. And in their respective worlds, both conclusions are correct. In the world of science, the Atheist arguments are powerful. Why invent a supernatural God when natural explanations can answer nearly every question about the physical universe? Keeping the uncertainties of a problem as few as possible is a very simple and very logical concept, and it works superbly. We don't know why the universe exists, why add a God, when doing so will merely add another layer of mystery? In the world of religion, the many theist arguments, which I need not repeat, are equally convincing. Despite scientific progress, there will always be some questions that reason and science cannot hope to answer. To state that life must have arisen by an extremely fortuitous accident because life does in fact exist and there is no other way it could possibly have arisen is hardly proper science. Scientific investigation has yet to demonstrate that an actual external reality lies behind the mental images we call the physical universe. How can it disclose anything about a hypothetical but likely God far more remote? IMO, whether a person is an Atheist or a Theist is an emotional decision based upon that person's particular psychological make-up, and not upon any discoveries of science. The emotionalism with which both sides defend their views speaks for itself. As for me, the day has ended, the cats are hungry, and I'm growing tired. That means it's time to shut down the shoppe and call it an evening. But I'll return tomorrow with fractal and philosophy. Until then, take care, and long live fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Midget_in_Lilac { ; time=0:02:00:02
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+1.92588928983815400/+0.00024206172436048\
/1137618/1/124.999 params=1/-1.618/1.618/-16.8/0/0
float=y maxiter=1200 inside=0 logmap=32 periodicity=9
colors=000RSV<3>Zfd`ifbmidqkftm<3>Ij4qls<3>m`mlYlkVj\
<2>hMfgJefIc<4>bGXaFVaFU<3>ZDO<4>WTNWWMVZM<2>UgMUjMW\
iL<3>ciJehJghI<2>mhH<7>RONOLOMJP<3>B9R<3>ZTf<8>EQqCQ\
rAQt<3>1Px<3>A`TCbLDaLD_KDZK`Hl<3>WIoVIoTJl<3>PLcOMa\
NNZFRHMNX<3>IQOHQLGRJJ8Y<3>HFRHHQGJO<3>FQIfmF<7>S`HQ\
_HOYH<3>GSH`ALWEKx4W<3>`2JV1GP1DSQLVmSE3t<3>VDeZGabI\
ZfLVjNSL7V<2>u6l<2>qcM<2>tqluuttoetiStcE<3>UWFNUFHTF\
GSGZdZMNrLOn_XGeaCje9mjDooH<7>TmRQmSNlT<3>ClX<3>YVPb\
RNhMLmIJrEI<3>eOObRQ_TR<2>R_V<3>`_cb_ed_g<2>k_m<8>QF\
ROCPLAM<3>C1D<5>POS
}
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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