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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal might show actual new material in the hypercomplex Mandelbrot set, or it might be an artifact of mathematical imprecision. But regardless of what it is, it's an image with spirals everywhere. There are single spirals, double spirals, even signs of triple spirals. In fact, the image is filled with spirals without end. And "Spirals Without End" is what I named it. The image is a zoom into a hidden valley that appears peeking between the converging straight arms of yesterday's "Hyperbud" image, where a new world appears to be only partly revealing itself. In contrast to yesterday's image, which suffered from resolution breakdown, today's image suffers from the near impossibility of finding an acceptable coloring. I finally settled on a very broad purplish palette, though the result still leaves much to be desired and drops the rating to a below-average 3. While fractaling, I sometimes wonder about the meaning of it all. Is the existence of fractals filled with a deep, as-yet-undiscovered meaning, perhaps about the nature of reality, or are fractals mere candy for the eyes? And what of the concept of meaning itself? Is it something invented by the highest known form of life on the planet Earth, or is the universe filled with it? Does meaning actually exist before a self-aware entity asks the question 'why'? Does meaning exist on a two-mile-wide chunk of ice orbiting in the cold loneliness of the Oort cloud, where observers never have and never shall venture to ask 'why'? And what of this fourth dimension with its hyper-objects? We can infer exactly how the various parts would fit together if it existed, but even knowing these things, we cannot visualize something as simple as a tesseract. Does this mean that the fourth dimension does not exist? Does it mean that it does exist but we cannot visualize it? Does it mean that we have invented the whole puzzle as a mental exercise? Or does it mean anything at all? Don't expect answers any time soon. And don't expect an image soon if you try to run today's parameter file. It takes 1-1/4 hours on my less-than-supersonic P-200 machine. The best way to see the puzzling image is to download it from Paul's web site at: Tuesday's fractal weather was cloudy and chilly here at F.C., with a high temperature of 34F 1C. The ex-dynamic duo passed the unsatisfactory day lounging by the heat, except for when they were asking for food. This morning has brought freezing rain, which is even worse. It's a good day to remain indoors and get ahead on some work. Until tomorrow, when things will hopefully be more pleasant, take care, and try to make the best of bad situations as they arise. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
SpiralsWithoutEnd { ; time=1:15:40.15--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot passes=1 center-mag=-0\
.04192332435179621/+0.08550882276013791/4021858
params=0/0/10/0/1e-014/0 float=y maxiter=20000
inside=255 logmap=-3100 periodicity=0
colors=0009ECAECBEDCEDDEDEEDFEDGGDHGFIGFJGFKGFLGFM\
GFNGHNGHMGHMGHMGHMGHMHHMHIKHIKHIKHIKHIKHIKHKIHKIHK\
IHKIHKIHKIHKKGMKGMKGMKGMKGNKGNMGNMGNMENMEPMEPMEPNE\
PNEPNERNERNDRNDRPDTPDTPDTPDTPDTPDVPDVRBVRBVRBVRBWR\
BWRBWTBWTBWTAYTAYTAYTAYVA_VA_VA_VA_V8_V8`V8`W8`W8`\
W8`W8bW8bW8bY6bY6dY6dY6dY6dY6d_6f_6f_4f_4f_4f_4g`4\
g`4g`4g`4g`4i`4i`4ib4ib4kb4kb4kb4kb4kd4md4md4md4md\
4md4nf4nf4nf4nf4pf4pf4pf4pg4pg4rg4rg4rg4rg4ri4ti4t\
i4ti4vi4vi4xk4xk4yk4yk4zk4zk4zm4zm4zm4zm4zm4zm4zm4\
zn4zn4zn4zn4zn4zn4zp4zp4zp4zp4zp4zp4zr4zr4zr4zr4zr\
4zr4zr4zt4zt4zt4zt4zt4zt4zv4zv4zv4zv4zv4zv4zx4zx4z\
x4zx4zx4zx4zy4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4\
zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx\
4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4z\
x4zx4zx6zx6zx6zx6zx6zx8zx8zx8zx8zxAzxAzxAzxAzxBzxB\
zxBzxBzxBzxDzxDzxDzxDzxEz }
frm:HyperMandelbrot {; periodicity must be turned off
a=(p1),b=(0,0):
q=sqr(a)-sqr(b)+pixel,
b=(p2+2)*a*b+p3,
a=q,
|a|+|b| <= 100 }
END 20.0 PAR-FORMULA FILE==================================
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