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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The hole at the center of today's image looks a lot like a classic Mandelbrot midget. It has a main bay, a main bud, a 'Seahorse Valley', and traces of smaller buds. But, even at a maxiter of 8200, its shore line is ill-defined, and East Valley, sometimes called 'Elephant valley', which is a defining feature of classic M-set midgets, is not even hinted at. Since the central hole in the image looks like a midget, but not a classic midget, I named the picture "The Unmidget". A random shape is normal for midgets in Mandelbrot fractals with an exponent of Z between 1 and 2. The exponent of today's fractal is the cube-root of 3, or 1.5874, which places it right in the middle of the 1-to-2 zone. For my investigation, I chose the second level below ground level of the parent fractal, which at this level resembles the midget in the image, except that the large bud points to the southeast rather than west. The area of the parent that I investigated lies in the upper-right branch of what resembles a Seahorse Valley. The image itself is filled with the irregular bits and pieces that characterize the low-order Mandeloids. These fragmentary bits of fractal stuff are not totally random, for a careful examination will reveal repeating shapes throughout the scene. Having nothing really exceptional to offer, the image could climb no higher than an average 5 on the rating scale. The image can be drawn from the attached parameter file, but because of the 15-minute render time, the better choice is to download the complete GIF image from the W.W.Web at: The Fractal Central weather today turned out sunny and chilly. The temperature reached no higher than 51F 10.5C, but with no wind it was comfortable enough in the sun to please the fractal cats. They spent over an hour chasing the sunbeams filtering through the holly trees. And I've got to chase down some missing photographs. While I'm searching the files, cartons and envelopes lying around Fractal Central, I'll be thinking deep philosophical thoughts. If anything comes of the thoughts, I'll report it in tomorrow's FOTD. If not, I'll at least have another quality fractal to offer. Until next time, take care, and celebrate something with a fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
The_Unmidget { ; time=0:14:59.02--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.500405232383985/-0.561425172652767/6\
746.955/1/-92.5/1.5597828584290596e-011 params=1.5\
874/0/-2/0 float=y maxiter=8200 inside=0 logmap=150
colors=060hK2jK1nWttXtuXtuLts9wr6tp6ro6on6km6hl7dk\
9ajCZfFVcGR`KNYLLUOGRRDOTALW6HZ2E_0Bb08c0Fe0Nf7ShF\
_iMdiRkkZrleumluosuotrmt`ltHmtIlsIlsIlsIksIksKkqKi\
qKiqKiqKhqLhpLhpLfpLfpLfpNeoNeoNeoNcoNcoOcmObmObmO\
bmO`mQ`lQ_lQZlQYlQXlQWlOVkOUiOVhNWfNXeNYdNZbL_aL`_\
LaZKbYKcWKdWKfVIhTIjRIlQHnPHpNHrMHtLFvJFxIFzGIyDFw\
GDtJBpL8mN5hQ0eP3cR8aVD_WI_ZNZaRXbXWe`WhdUijTlnRor\
RpuQsuOtuOtuNsuLpuKlqKinJejGbgGZcFW`DRXDPUCLQAIO9G\
NAFNAFNAFNAFNAFNCDNCDNCDNCDNCDNDCNDCNDCNDCNDCNDCLF\
ALFALFALFALFALG9LG9LG9LG9LNmLQmLQmLJ7LJ7LJ7BJ0LJ7U\
DFaAMf7ek6ur6yu6zu6zr6yn6xh6wh6vg6uf9qdGkcJdcKkaLq\
`Lq_NtYNtYOtXOtWQtUQtSRtSRtRTtQTtOUtNUtNUtLUtKWtIW\
tHWtHWtFWtFWtEXtEZtE_tD`tDbtBctBctBctAetAet8et8ft8\
ft7ft7ht5ht5ht5ht3it3it2it2it2it0it0it0it3it5it7it\
8itBitDitEitFitIitKitLitNitQitRitSitUitXitYit_it`i\
taitcitcitditfitfitgithit
}
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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