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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's FOTD I tackled the center of the fan that appears in yesterday's image, which is the parent fractal of many midgets past and future. The midget in today's image was not as hard to find as I had expected. The fan-like feature in the parent fractal is filled with holes as well as discontinuities. I began my search in one of the holes that was not broken by a discontinuity. I found a symmetrical pair of features almost at once, with the midget lying at the center as expected. When I found the midget, I was almost disappointed at how easy the search had been. There must be more than this around, I thought. Then I noticed that the midget was surrounded by a whole flock of symmetrical features, each apparently with a midget at the center. I chose a likely feature in the northeast suburbs of the larger midget and found the midget of today's image at the center. The picture, which I have named "A Midget from the Fan" is an interesting one to color. The broad palettes that work so well on most midgets don't work at all on today's strange little fellow, which turns boringly flat. Instead, I used a totally random palette, fine tuning only a few registers. The result is a patchwork but still attractive picture that rates a perfectly average 5. With a render time of almost 14 minutes, the parameter file is uncomfortably slow. But there is no need for concern, as the pre-rendered GIF image file has been posted to Usenet at the site: The fractal weather today was cloudy and cool with just enough occasional light rain to keep things damp. The dampness and temperature of 68F (20C) combined to keep the fractal cats safely ensconced indoors. I pondered a bit this afternoon about the unending debates between believers and skeptics. The debates go on and on, never reaching a conclusion, neither side winning or losing, both sides certain that they are right. How can such an illogical situation exist among logical people? In my opinion, the disagreement springs from the different world views of the opposite sides of the debate. The debate is basically a continuation of the age-old conflict of Materialism vs. Idealism. Idealists and materialists sometimes take the same facts and reach exactly opposite conclusions from them. Take for example the factual statement "heaven exists in the mind". To a materialist, who considers only objective things real, this implies that heaven does not exist. But to an idealist, who considers subjective things as real as objective things, but on a different level, the statement gives the actual location of heaven. "Of course heaven is in the mind," the idealist might answer. "Where did you expect it to be, in the vacuum of outer space?" Knowing that heaven is a mental construct, the materialist is satisfied that heaven is not objective, and therefore is unreal, does not exist, and will never be experienced; while the idealist considers heaven to be a different kind of reality, which like a dream is unreal when a person is physically conscious, but becomes a real experience when the level of consciousness shifts. An idealistic world view does not necessarily imply a belief in the supernatural things of religion, or the existence of life after death, but it removes many of the philosophical obstacles to acceptance of these things. This is enough philosophy for one day. There are many days and much philosophy to come, however. And speaking of being ensconced, I'm about to ensconce myself in my overstuffed chair for some heavy TV watching and dozing. But I'll return tomorrow right on schedule with another FOTD to amuse, entertain, and enlighten. Until then, take care, and don't let a failed fractal get you down. Jim Muth jamth@mindspring.com |
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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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