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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: What number lies halfway between one and two? Let us call that number X and say that today's FOTD is a scene in the Z^X+C Mandeloid. The midway location of the exponent of Z is the exact reason I named today's unusually rich fractal image "Halfway There". At first glance, the puny little Z^(1.5)+C figure invites nothing more than a tap on the <esc> key. But sometimes first glances are deceiving. The shriveled little fractal is filled with discontinuities, but it does have areas of quasi-chaos that hold some interesting images. Perhaps the most interesting area of this curious figure lies at the north and south extremities. This afternoon I chose the north end to explore, where several tiny midgets are located. When I had filled the screen with one of the more remote midgets, I zoomed in on the shoreline of this midget to find an even smaller midget. Since Mandeloids generally have one less lobe than the exponent of Z, the Z^1.5 figure has 1/2 lobe, and the hard-to-find midgets within it also have 1/2 lobe. Now, a half-lobed Mandeloid midget might sound like an absurdity. I assure you it is not. These midgets can be quite fascinating. Today's picture for example is notable for the spiral arrangement of features surrounding the oddly-shaped midget. This spiral arrangement gives the impression that we are seeing only part of the scene, that the complete fractal skews off the screen into imaginary planes much as do the images created with complex exponents. Whatever the case, due to the unusually large maxiter, the parameter file is rather slow, requiring an overnight rendering on a tired old 486 or 1/2 hour on a frisky young Pentium. The cure for any impatience is to download the image from: The unimportant but always interesting weather was perfect today, with crystal blue skies, puffy white clouds, and a temperature of 77F (25C) making it optimal for fractals. Between lawn-trimming and fractal-hunting I had little time to ponder the big questions today, but the muse will reappear in a day or so. For now, depending on where you are, have a pleasant evening or morning. Until tomorrow, take care, and see you then. Jim Muth jamth@mindspring.com |
START FORMULA==============================================
MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16
}
END FORMULA================================================
START PARAMETER FILE=======================================
Halfway_There { ; t=0:21:32.34 on a p233, SF5
reset=2000 type=formula formulafile=slices.frm
formulaname=MandelbrotN center-mag=+0.01891867191850\
896/+0.59812610863641660/8.092122e+010/1/14.999
params=1.5/0/0/0/0/0 float=y maxiter=64000 bailout=25
inside=0 logmap=1600 symmetry=xaxis periodicity=10
colors=000FKINm9XVeW`SVfERSTTbEU4HVJBVY5xDgiVMsdjfhN\
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}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Halfway_There { ; t=0:21:32.34 on a p233, SF5
reset=2000 type=formula formulafile=slices.frm
formulaname=MandelbrotN center-mag=+0.01891867191850\
896/+0.59812610863641660/8.092122e+010/1/14.999
params=1.5/0/0/0/0/0 float=y maxiter=64000 bailout=25
inside=0 logmap=1600 symmetry=xaxis periodicity=10
colors=000FKINm9XVeW`SVfERSTTbEU4HVJBVY5xDgiVMsdjfhN\
BR2IZ1Pe0oJ0kyKbrAKTYJ25PQ25RkEZWNeGEQaKYPQeC`_boVy\
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}
frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16
}
END 19.6 PAR-FORMULA FILE==================================
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times.
