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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: There is a 'zexpe' fractal -- the fractal formed by the formula Z^2.7182...+C, and named by Lee Skinner. Now we have a 'zexpi' fractal, which naturally is formed by the formula Z^3.1416...+C. Like all fractals created from fractional powers of Z, the zexpi fractal is infinite in surface extent as well as depth. The MandelbrotBC1 Fractint formula can explore the more remote parts of the infinite surface extent of these fractional fractals. Setting the real(p2) parameter to the number pi, causes the formula to draw 'ground level', but who wants to sit at ground level when there are limitless heights to scale? For today's fractal I went up 189 floors from ground level, until I found a level where the zexpi fractal really does things. The midget at the center of today's image lies in the suburbs of a larger midget, which lies in the suburbs of a still larger midget, and so on about 6 times, until we reach a midget that lies in an area of chaos on the northwest shore of the main bay of the parent fractal, which is the one mentioned above, that really does things. I named the image "Pi in the Sky" not in mockery of religious beliefs, but rather because it is an accurate description of the image and its location in relation to the entire infinite fractal. The rating of the image is not quite as high as its location, but with a rating of 5 the image is worth the effort of running the parameter file, or the lesser effort of downloading the image from: The fractal weather today featured a big warm-up, with brilliant sunshine and a temperature of 77F 25C. The fractal cats took up residence on the porch before lunch time, and stayed there until near sunset. I'm still studying the series of messages recently posted to the Philofractal list by the Programmer Dude. I can find little to disagree with in his messages, which largely mirror my own views. My world view is that only an infinitesimal part of reality, if such a thing actually exists, is presently known, and that most of reality is unknowable. I feel it is likely that man's existence extends beyond the physical world. I doubt that miracles happen, especially the greatest miracle of all -- the miracle claimed by materialists when they attribute man's inner world with its unlimited variety to the activity of the pound or so of mush known as the physical brain. I am now convinced that precognition does exist. At the same time, I remain convinced that most of the popular occult and paranormal things are more entertainment than fact. I doubt that off-planet aliens are visiting earth. I feel that alien abductions are misinterpretations of normal sleep phenomena. I am convinced that out-of-body experiences and lucid (waking) dreams, which I sometimes have, are real, but that they can be interpreted in several ways. Finally, I am a Theist, but my idea of God is so abstract that it cannot be put into words. That's it for now, fractal fans. Until next time, take care, and we don't even know what we don't know. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Pi_in_the_Sky { ; time=0:17:28.25--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-0.89071956777594660/+0.395577680067524\
30/1.086197e+012/1/45.000916072899642/-0.007023192\
99345871562 params=3.14159265358979/0/189/0
float=y maxiter=3600 inside=0 logmap=518
colors=000jCZlFXmHUoKSqNQrPNtSLvVJwXGy_EzaCw_BuYBs\
WBqUAoSAmQAjO9hM9fK9dI8bG8`E8ZD8XG7VI7TK7RM7PO7NQ7\
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kYom_vo`wqPysDzu1ww2ux2ry2pz3mz3kz3iz4fz4dz4az5_z5\
Yz5Zz9_zD`zHazLbzPczTdzXez`fzdgzhgzkeziczhbzf`ze_z\
cYzbXz`Vz_TzZSzXSzL`zUhza
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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