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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The word has come in to Fractal Central that fractals *might* exist on other planets. The question now becomes whether a fractal really exists if no intelligent life is there to be aware of it. Perhaps a better way of stating the question is to ask whether fractals existed on earth 2000 years ago, before we knew of them. And this is simply another form of the old philosophical question of whether we create reality by considering certain things of which we are aware to be real, or whether the things would be real even if no intelligent life existed to be aware of them and declare them real. Today's modest offering most certainly is real. (I think.) It is an example of a very common fractal feature I call a 'dry lake'. All too often while tracking down a midget, I come upon features of a class I call 'dry lakes'. One of these dry lakes exists at the exact center of today's image, and is the reason I named the picture "Dry Lake". A dry lake is surrounded by the symmetrical type of features that point the way to a midget, but before the midget is reached, the basin bottoms out in a saddle-shaped surface. These saddle surfaces indicate a failed search, and as soon as I see one, I usually turn away to search elsewhere. I consider these dry lakes to be near misses. A midget does exist nearby in the surrounding Julibrot, but the slice on the screen misses the midget by a narrow margin. Still, if the slice comes close enough to the actual midget, some of these dry lakes display nearly perfect surrounding features. In these cases, the presence or absence of a central midget makes little difference. But I sometimes wonder whether a program designed to automatically track down midgets would be fooled by these dry lakes. Today's image, which misses the midget by a rather wide margin, shows a relatively imperfect dry lake, with symmetry that is unbalanced and does not go beyond the stage of 2. Because of its imperfection, I rated the image a below-average 3. With a render time of 15 minutes, the parameter file tries one's patience. A download of the GIF image is the way to see today's FOTD. That download will soon be available at: The fractal weather today here at Fractal Central may safely be passed over. But for those who have an interest in such unimportant things, it was another perfect day, with blue skies and a temperature of 84F (29C). The cats were happy all day. It's now time to do other things. So until next time, take care, and we have the fractal saddle, all we need is the fractal horse. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Dry_Lake { ; time=0:14:59.68--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.63371185168602/+1.1142664608147/1.59\
2733e+007/1/67.5 params=10/-1.333/1/-13.33/-2/300
float=y maxiter=1200 inside=0 logmap=246
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}
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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