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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Believe it or not, I have just received a telephone call apparently from India, informing me that I have been randomly selected to receive a free cell phone. It is a mystery why the phone company had to go so far afield to let me know of my good fortune. Perhaps they are seeking cheap labor. Or perhaps they are a clandestine alien scout team from another world that has come to irradiate our brains into non-functionality, so that we will be unable to offer effective resistance when the main invasion force arrives to enslave us.  Of course, they could do this just as easily by addicting us to fractals. Today's fractal image shows a Mandelbrot midget that can't get its math right. It is a quadratic midget surrounded by six identical features rather than the expected four. The iterated formula combines portions of Z^(-1.5) and Z^(-4.5) then adds (1/C) to produce another of those sprawling fractal. Today's image was found in a valley of its parent. Judging from the bug-eyed double-spiral features that infest the image, the valley in which it lies must have 'East Valley' characteristics. I have no idea why the expected 2,4,8... series of elements has broken down. Maybe the series is still there, but has been disguised by the inconsistent sizes of the features. I named today's image "Miscount" in reference to the wrong number of features around the midget. The image rates a 6, which would appear to be justified. The render time of 5 minutes may be cut drastically by downloading the pre-rendered image from the FOTD web site at: Unfortunately for any philosophy fans who yet have hope, my philosophical views are undergoing a change, which I will need to work out. My mistake was that I promised earth-shattering conclusions at a definite time. The philosophy will eventually appear when I get it right. I have no idea when that will be. At this point, my conclusions are so far out as to appear kooky. I am not particularly offended at being considered a kook, but kooky claims, especially earth-shattering ones, must be at least a little believable. With a high temperature of 48F 9C, heavy clouds, blustery winds and occasional light showers, Sunday was anything but spring-like here at Fractal Central. The cats returned inside after only a few minutes in the yard. I had my nose in my book most of the afternoon. The next FOTD will appear here in 24 hours. Until then, take care, and be alert. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Miscount { ; time=0:04:58.14--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+2.44071194518632700/+0.111691600345395\
40/693633.5/1/132.5/5.05031376163422863e-008
params=-1/-1.5/-0.25/-4.5/0/0 float=y maxiter=1000
inside=0 logmap=87 periodicity=10
colors=000FRzGTuHQvIMwJJxJGxPMxUSx_Yxdbxjhxonxutxz\
yxrwkkv_cuOXtCQs0Tp1Vm1Xj1Zg1`d1ba1e_2gX2iU2kR2mO2\
oL2qJ2pG6pEAoCEoAIn7MzZQz3UmZrl4Yk6zj9_iB`hDagGbgI\
cfKdeNedPfcRgbUhaWiaYiaWjaUkaTkaRlaPmaOmaMnaKoaJoa\
HpaGp`Ii_KbZMWYOPXQIWSBWT5ZR9`QDcOHeNLgLPjKTlIXoH`\
qFdsEhvClxBpzAtpIjfP`XWRNbHEi8EfBEcDEaFEZHEXJEULER\
OEPQEMSEKUEHWEFYJIZNKZRNZVPZZRZbUZfWZjYZn`ZrbZvdZi\
YZfZYdZXb_W`_WZ`VX`UVaTTaTScRSdPSfNRgLRhJRjHQkFQmD\
QnBQo9SjATfBVaCWYDYTEZPF`KGaGHcBId7Je3K`6LW9LSCMNF\
MJINELNAOO5RO1UOD_ZOehZjrWenT`jQXfarkbsibsgctectcd\
uadu_duZYoUSjPMeKF`F9WA3R5FVBRYGa`LZYQXWVVT_TRdRPh\
dsZfkVhdRjYNlQJnJFpCBkBHfBMaARXAXS9aN9fI9kHGiHMgGS\
eGYcFdaFj_EpYEvW9wO5xHByGHzGMzFSzFYzFbzEhzEmzEnzFo\
zGpzDqzBrz9sz7tz5uz3vz6wz9xzByzEzzHzzJzzMzzOzzRzzU\
zzWzzZzzazzczzfzzhzzfzzdzzezzezzezzfzzfzzfzzfzzgzz\
gzzgzzgzzhzzhzzhzzhzztzzt }
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 PARAMETER FILE=========================================
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times.
