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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's FOTD pictures another midget in the fractal that has been producing so many strange midgets lately. But is it a midget? That's what I wondered as I studied the scene, searching for a name. The answer is both yes and no. The indecision lowers the rating to a 6. The eight open areas actually resemble things one might see in a Julia set more than they do Mandeloid midgets. Yet the sharply defined surroundings have a kind of Mandeloid feel to them, and the image is indeed oriented in the Mandelbrot direction and located in the critical plane. The answer is simple. The visible image contains no quadratic midget, for none is visible. At the same time, the image does contain a midget, but the midget is far too small to be seen. What the image shows is the ring of 8-way symmetry surrounding a midget, which is located far down in the center of the image, where the spokes come together. At this time I can only imagine the ultimate appearance of the midget, which lies at a magnitude around 10^20, but I am placing today's image in my file of currently unreachable goodies, and holding it until Fractint or some other fractal generator comes out with arbitrary precision math for user-written formulas. Until that time, there is no hurry. The reachable fractal world at a magnitude of less than 10^13 is large enough to keep me busy for at least a million years. The parameter file attached to the bottom of this letter runs in 12 minutes; the GIF image that will soon be available at: The fractal weather today continued in the summer doldrums. The sky was so hazy that any clouds were invisible, the atmosphere was humid, with a temperature of 86F 30C. The cats slept most of the day. Looking at my desk top, I see enough work to keep me busy for at least 1/2 hour. The urge is great to put that small amount behind me, so the obvious thing would be to get started. Until next time, take care, and there will never be a last fractal. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Is_it_a_Midget { ; time=0:12:13.20--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=b
center-mag=+0.49712894345224910/+0.000002217255914\
71/1.116919e+011/1/-35 params=1/3/-0.35/4/0/0
float=y maxiter=12500 inside=255 logmap=789
colors=000N1KN1KP2KR3KT4KV5KY6K`7Kf5Kl4Mr3Ux2awAcw\
IevPgvXiudkukmtsotzpzzzzzzN5dOD`OKXPRUPYQQdMQkJSgG\
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pMBrGBRKL0NV7MPDLJJKDPK7VMF_NNdPViQbnSjsTrRR2KS2uW\
0JUTOkuNagSYaPbTMgLJlD000
}
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.
