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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Sometimes, perfectly good fractals turn into a mass of bits and pieces -- flinders that is -- and today's image is a perfect example of this fractal disintegration. I started with a perfectly good fractal -- the figure created by the formula Z^1.5874+C (the 1-1/2 root of 2) -- and investigated the area 6 levels up the logarithmic spiral. I chose a perfectly ordinary appearing valley to delve into, but I had not gone far when the whole fractal world disintegrated around me. Such disintegration usually signals a dead end of the search. Not in today's case however. This left-over chaos is filled with debris, which in itself forms recognizable repeating patterns. And as an added attraction, the chaos is overflowing with deficient midgets of all sizes and shapes. The overall effect of the image is one of fractal flinders floating in a vast space near a relatively unimpressive midget. The pieces almost appear to be drawn down into the midget as though it were a black hole. I first thought of naming the image "Black Hole", but decided on "Fractal Flinders", a title with a more attractive sound. The 16-minute render time will leave some impatient. The 1-minute download of the finished GIF image from the W.W.Web at: The fractal weather today featured blue skies, puffy cumulus clouds, gentle breezes, and a temperature of 79F 26C. All in all it was a perfect Autumn day, which left the fractal cats purring with contentment. No philosophy will be lost while the Philofractal list is down. I'm still writing my thoughts, and saving them in a separate file. The accumulated wisdom will appear as soon as the philofractal list is once again up and running. That's it for today, fractal fans. It's time to shut down the fractal shoppe and call it an evening. But the next FOTD will appear in two wags of a . . . a pussy cat's tail. Until then, take care, and I have not yet begun to explore. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_Flinders { ; time=0:16:31.13--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.51849225088358700/-0.546491304449809\
/24561.24 params=1.5874/0/6/0 float=y
maxiter=36000 inside=0 logmap=254
colors=000_Q0`R0`S0_R0ZQ0WP0VN0UN0SM0QL0PK0NI0MH0L\
H0KG0i_lfDidHkdKkdNlcQlcUmcWmc_nbbnbepbhpbkp`cb`WQ\
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qSzpUzpUznUzmVzlVzlWzkWziXzhXzhXzgZzfZzd_zd_zc`zb`\
z`bz`bz_bzZczYczYdzWdzVezUezUezUdzUdzUczUczUczUbzU\
bzUbzU`zU`zU`zU_zU_zUZzUZzUZzUXzUXzUXzUWzUWzUWzUVz\
UVzUUzUUzUUzUSzUSzUSzURzURzURzUQzUQzUPzUPzUPzUNzUN\
zUNzUMzUMzUMzUMzUMzUMzUMz
}
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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