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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: No, today's image, with its fractional rating, is not pretending to be an artsy film; it's an image that I just couldn't decide how to rate. When I decided to rate the image at an 8, I felt I was short-shrifting it. Then when I decided on a rating of 9, I felt I was over-rating it. The rating of 8-1/2 seems just about right. I named the image "Vitality". A brief glance will show why. The formula behind the image, -1.05(Z)+1.05(Z^(-2))+(1/C), draws a fractal that consists of two contrasting Mandeloids in a NW to SE oriented line. The NW Mandeloid has an oversized main bud, while the main bud on the SE figure is undersized. There must be a rational mathematical reason for this particular type of distortion, but I'm not aware of what that reason is. Today's tiny midget is located in a disconnected hole near the tip of a filament extending from a minor bud on the N shore of the main bud of the NW Mandeloid. When rendered with the usual equal-iteration bands, today's image is acceptable, but the <atan> option really brings it to life. To see the living fractal, run the attached parameter file and see it in 2 minutes, or wait an hour or so, then go on the internet and download the image from: The fractal weather today was cloudy and very humid, with a temperature of 83F 28C and occasional rain. The fractal cats complained but accepted their confinement. I must now accept that the work before me needs to be done, and the only way I know to finish the job is to start it. When the work is finished, I'll be here with another fractal and perhaps some philosophy. Until then, take care, and be good but not too good. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Vitality { ; time=0:02:13.97--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.02922892649398737/-0.022688490365579\
9/2.024055e+012/1/-125 params=-1.05/1/1.05/-2/0/600
float=y maxiter=1200 inside=0 outside=atan
colors=200ZzxSzxNzxIzxCzx7zx2zx2zx2zx2wx7qxFlxNgxW\
bxcYukTptOmzJiwGsrExmDxjBxk8xm6xo4xs1wy0nt0cg12_02\
S0200200200300600A2RamzxcqsUakPLc24XkTxhNxgIseDpc8\
kb1f`0cZ0ZX0WzhUzmQzrPzwN`OxbNxcLxeLxgJxhIxjIxkGxm\
EwoEupDsrBrrBpmGrjJreNrbQrZTrUXrR_rMbrIfrFirAlr7pr\
3sr2su2tw2wx2wxcIsZOuUVuPawMgxHnxCtx9zxAxwAwsAtpCs\
mCqiCpfCncElZEkWEiSFgPFfLFdIFbFHgAIl6Kp3Mt2Nx2Pz2R\
z2Sz2Uz2Wz2Sz2Rn2P_2NL2M62I22H12F08E0GC0P90Z70f50p\
30x20xA0xH0xN0xW0xb0xh0xp0xw0xz0xz0xz0xz0xz0xz0xz0\
xz0xz0xz1xz2xz4xz6xz8xz9xzBxzGxzLxzOxzTxzXxzaxzdwz\
iszlrzqpztnzidp_XbONNEFA46MX2Xw2Zs2Zp2`n6`kDbiIbfP\
cdWca`e_feXkgVrgRxhQxhNxhLxkJxoJxrJxuIxyIxzIuzGrzG\
nzGkzGizIhzJfzLduNcpOamQahR`cTZZVXUXWPYUMYUodNziGz\
nLpqQctWewZgxahxdhzhjzkkznmzrmzuozxpzxrzxrzxtzxuzx\
uzxjzxZzxNzuCzn2zh2za2zc5zcCzdIzdRzfXzfczfjzhrzhyz\
izzizzizzmzzntzrozsjzwczx
}
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.
