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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The FOTD for July 2, which, due to a power failure, was finished too late to be the FOTD for July 2, now appears as the FOTD for July 3. I named the picture "The Smallest Midget", not to be confused with "The Littlest Angel". The 'smallest' in the name refers not to the size of the midget, but to the exponent of Z in the formula that drew the midget. With an exponent of only 1.15, the function of today's fractal is perilously close to being linear, and linear functions do not produce fractals. But thanks to the 'Branch Cut' formula, we can go as far out the logarithmic spiral as necessary to find an interesting section of the infinite fractal, which seems to expand and become ever more detailed the farther out we travel. In today's case, we travel out 320 turns, to where the parent fractal resembles nothing as much as an egg with just about the longest tail ever seen. Today's midget lies about halfway out that mammoth tail, and finding it was no easy task. The shape of the midget quite accurately reflects the shape of the parent fractal, humungous tail and all. The excessive maxiter is necessary to fully define the midget, which at a lower maxiter has sections where the surrounding chaos appears to blend smoothly into the midget rather than form a well-defined sharp edge. I colored the inside of the midget a brilliant white instead of the normal black. This way the midget reminds me of the candles that kept Fractal Central illuminated last night when the entire area was blacked out. The stream of chaos trailing from the midget could almost be taken for the column of heat rising from a candle flame. I rated the picture at a 7. The picture is worth it considering the extra attention I gave to its coloring. And with a render time of 11 minutes, running the parameter file does not try one's patience beyond endurance. Of course, the GIF image will soon be available on the internet at: The fractal weather today was as good as it gets around here, with the bluest skies and a temperature of 72F (22C). These conditions made the fractal cats happy, much in contrast to yesterday, when a violent thunder-storm struck in the evening, with winds of near 120kph, torrential rain, continuous lightning and even a scattering of hailstones. When the wind and thunder finally died down, the cats didn't show themselves for over an hour. Luckily, it was a Sunday, with little computer work to be done when the power failed. It's now Monday evening however -- time to give the cats their end-of-day snack and shut down the fractal place until tomorrow. Until then, take care, and weather is supposed to be chaotic and even fractal in nature, but I saw no fractal midgets in yesterday's storm. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
TheSmallest_Midget { ; time=0:11:01.14--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-12.88324182229829000/-10.9467020423215\
4000/4045361/1/150 params=1.15/0/320/800 float=y
maxiter=75000 inside=255 logmap=94 periodicity=10
colors=000K0AK0AK0AK0AK0AK0AK0AK0AK0AK4AK7AKBAKEAL\
IAOLARPAUSAXVA_ZAbaAeeAhhAklAnoAqrApm9pi8pd8p`7pX7\
pS6pO5pJ5pF4pB4lC8iDCfDFbEJ_FMXFQUGTQHXNH_KIcHJfDJ\
jAKm7Lq4LtKOq_RnbUkd_hUdeJjb8g`JfrTlzPqwLqwIqrJccK\
_ULXKLUBKTBJRBIQBHOBGNAFMAEKADJACHABGAAFA9DA58A8CA\
7AA69AgoCcmB_kBWiBVgBVeBUcBTaBS_BRYBRWBQUBPSBOQBNP\
BNOBMOBLNBKMBKMBJLAIKAHJAGJAGIAFHAEGADGACFACEABDAA\
DA9CA8BA8AA7AA6FA5KATPKSUUSZcR_iRZnQZnQYmQYlPZkP_k\
O`jOaiObhNchNdgMefMfeMgeLhdLicKjbKkaKlaJm`Jm_InZIn\
ZIoYHoXHpWGpWGqVFqUFrTFrTEsSEsRDtQDtQDuPCuOCvNBvMB\
wMBwLAxKAxJ9yJ9yI9zHAzGCzGEzFGzEIzDKzDMzCOzBQzARzO\
SzNTzNUzMVzMWzMXzLYzLZzL_zK`zKazKbzJczJdzJezIfzIgz\
IhzHizHjzHkzGlzGmzGnzFozFpzFqzErzEszEtzDuzDvzDwzCx\
zCyzCzzBzzBzzBzzAzzAzzYzzXzzXzzWzzWzzVzzVzzUzzUzzT\
zzTzzSzzSzzRzzRzzQzzQzzQzzPzzPzzOzzOzzNzzNzzMzzMzz\
LzzLzzKzzRzzYzzdzzkzzlzzz
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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