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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I expected to have an easy day today, but an unexpected rush job came in from the Kung-Fu customer, which kept me busy all afternoon. As a result, I had to totally forego the planned philosophical discussion -- and that's reality. But I still managed to find a respectable fractal, which I now present as the FOTD for October 05, 2000. A dingbat is one of those old-fashioned decorative ornaments, often resembling leaves on twisting vines, that in the past were used in printing to mark chapter beginnings, etc. Something about today's image reminds me of one of those ornaments, so I named the picture "Dingbats". The image rates a 6. I cannot give it more than that after spending only 10 minutes locating and coloring the scene. The midget at the center is fully resolved -- the distortion is caused by the exponent of Z, which is 2.01 instead of 2. The image was calculated by the MandelbrotBC formula, which draws scenes in the more remote parts of the infinite hyperspirals created by fractional powers of Z. The render time of 10 minutes makes a download of the GIF image file the wiser choice. That download may be found on Usenet at: The fractal weather today was sunny, warm and humid, with a temperature of 88F (31C), which was more like July than October. The fractal cats showed little eagerness to go outdoors in the afternoon heat, which was convenient, as I had little time to let them go out. The philosophy about the nature of reality went nowhere. The day has now ended with a whimper instead of a bang. It's time to shut down the fractal shoppe, comfort the cats, and call it an evening. Until tomorrow, take care, and where did these things we call fractals come from? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Dingbats { ; time=0:10:46.60 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1
center-mag=-0.93122846901060440/+0.08188815727122345\
/1.535833e+009/1/-2.5 params=2.01/0/32/0 float=y
maxiter=1800 inside=0 logmap=251 periodicity=10
colors=00000`00`00a00c<2>14h42i71k90lB0nE0n<2>L0sN0t\
Q0tT0vV0xY0y`0za0za0va0sa1na6kaAfaEcaI`aOWaTTaYO<2>a\
kEaoBcqIcqOcsVcsacthctncvvcvzcxz<2>dyzdztfznfzhfz`hz\
VhzOhzIizDiz6iz0kz0<2>kz0ky0it0hn4fh9d`DcVHaSKYRKWVL\
QWNN`OHaQEcQAfO7kO1lO0oO0nO0lO0hQ1dRBcTIaVQ`WYZWdWYl\
VZtT`zRazQczOc<2>zKNtII<3>QD0IB0BA04A00B00B00D00D10E\
60E92GD4GG<2>97OA4RB1VD0W<2>H0dI0hK0iL0fL0dL0cL0aN0`\
N0ZN0WN0VO1T<3>O7NLARIBVHEZEGaDHdAKi9Ll6Oq4Qt1Rx0Vz0\
Wz0Yz1`z7atDdnIfhOh`VkV`lOfnIhiNhdQi`TiYWkTZkOalKdlH\
hnDkn9nn6qo4ss1vt0yv0zx0zy0yz0tz0oz0lz0hz0cz0`z0Wz0R\
z0Nz0Kz0Gz0Bz09z04z00z00z70zE0<2>yc0vi0tn0nk0hiAafIW\
dTQccK`lKZxLZzNYzOWzQWzRVzTVzVTzWTzYRzZRz`QzaQzcOzdO\
zfNzhNziLzkLznNzqNztNzxOzyOzzOzzOzzQz<3>zRzzRzzRzzTz\
<2>zTzzQzzOzzLzzKzzHzzGz<5>z2zz7zzozznz
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(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| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
