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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's image we return to the most prolific of all formulae -- the MandelbrotMix4. This formula automatically initializes Z to a critical value and plots the corresponding Mandelbrot plane, an action which produces images filled with Mandeloid midgets of almost limitless variety. The formula 2(Z^(-0.875))+0.02(Z^(-18))+(1/C) drew the image, which was rendered with the outside set to <tdis>. The parent fractal appears as a crescent island with a large Mandel-bay on the west shore and mini bays stretching along the shore from southwest to southeast. Today's midget is located a short distance inland of the southeast coast. I named the image "Chaotic Toyland", a name with a slightly sinister sound, which matches the vaguely unpleasant image. I rated it a somewhat conservative 6. The parameter file file renders in under 5 minutes, while the GIF file downloads in less than half that time. In an hour or so, the GIF file will be posted to: Rating the FOTD images brings up a curious point of statistics. When I rate my FOTD's, I compare them with only my previous FOTD's. How then, can my average image be above average? If my average image gets better, the average itself gets better. In Lake Wobegon it is possible for every child to be above average, but such politically correct thinking will not work with fractals, because fractals exist in Fractal Land, which is far more dependent on accurate math. Of course, if I compared my images to all the images created by all the fractalists of the world, every FOTD could be above average. However, that would not be politically correct. My humility prevents me from admitting that I am the world's best fractalist.  The fractal weather was once again ideal for the pair of intrepid cats, who spent the afternoon enjoying the sunny skies and temperature of 77F (25C). When they finally came indoors I treated them to a dish of tuna fish. I have the day's philosophy all composed and ready to post. But as I now read it one final time, I realize that the words I have written come across as an attack on science, and I do not wish to attack science; I love science and the scientific way of doing things. My debate is not against science, but rather against scientism, a philosophy which assumes that questions such as the existence of God and the human soul can be answered by scientific methods. Science itself is based upon an unprovable metaphysical assumption. It is unwise for those who would defend science to do so by denigrating metaphysical things. It's now time to open up the fractal shoppe and begin the day's work. Until next time, take care, and think critically about your fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Chaotic_Toyland { ; time=0:04:40.44--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-1.39890905931845/-1.978045199630535/1.\
065885e+009/1/-60 params=2/-0.875/0.02/-18/0/800
float=y maxiter=750 inside=0
outside=tdis logmap=yes periodicity=10
colors=000Y5zb5z`5z`5z_5v_5rY5nY5iW5fW5bW5PW5CWF0b\
5RDP`ARW9ST7SP6UK4WH2WD0Y90Y60_20`00`00b00d00d00e0\
0e04_0KU0bP0nK7pIAmHCiFFfFHbEK`CMYBNVBRR9TN7WK5YI5\
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5zK5yN5vT5pW5k`5fd5bi5Ym5Tp5Pr5Mr5KrBItHFtNDtSCv_A\
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x09x7NxMbxTmxUywNwrMumKshKqcIoZImVHmSHmNFmHFmBDm5D\
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FT0FP0EM0CI0CF0BA0970040000000000000040590AD0BI0CN\
0ET0EY0Fb0Fg0Hm0HrNSzTRzWPz_NxbMpfKkiIdmHYpFRtEMxC\
FzB9z92z90vI0iR2_`4Ni6Cr92xA0xC0xD0xI0xM0xP0sT0nW4\
g_7`bAWfFPiIKmMEpP9tNCtNExNFtNHzMKzMMzMNzMPzKSzKUz\
KWzKYzI`zIbzIdzIezPYzVPz`HzfBz`EzYFzVIzPKzMMzIPzDR\
zAUz7Wz2Yz0`z0bz0dz`bzb`z
}
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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