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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's lively fractal was created by the mathematical formula Z^(-11)-11Z^(-1.1)+(1/C), and calculated by the fractal formula that I call MandelbrotMix4. As are most of my fractals, the scene is one of a midget Mandelbrot set lying in a vastly larger parent fractal. This parent fractal is better seen than described, but basically it consists of a fractal 'fan', with a spike extending out from the fan along the positive X-axis and a ring at the end of the spike. Today's midget lies in the suburbs of a larger midget, which in turn lies in the eastern extremity of the ring. I named the picture "Fractal Peanuts" because of the many peanut-like shapes infesting the area. I rated the picture an above average 7 because in my opinion it is above average. And yes, I did enhance the colors a bit in a graphic program, but this is no cause for concern, because I saved the enhanced version as a GIF graphic, imported it into Fractint, saved the enhanced color palette as a .map file, and applied the enhanced colors to the original image. Then I made the parameter file from the color-enhanced image, which means that the enhanced colors will be seen regardless of whether the image is rendered from the parameter file or downloaded from Usenet or the Web. For those who choose to run the parameter file and wait 6 minutes, the file is attached to the bottom of this letter. Those who choose to download the GIF image file from Usenet will find it posted to the binary group: The fractal weather today was perfect. This perfect October is making up for the far-from-perfect Summer that just ended. The fractal cats must agree, for they spent the afternoon in the yard, guarding the marigolds from butterflies and keeping the local raccoons at bay. My philosophy about life and death continued to ripen through the day, but it's not yet finished. If all goes as planned, the finished product will appear on the Philofractal list around the end of the week. I'm not going to hurry it and unintentionally offend those who see things differently. Nor will I water it down to a mush that will offend no one because it says nothing. I will try to walk the narrow line between the extremes, and also make at least a slight connection to fractals. And now it's time to shut down the fractal shoppe, give the cats their nightly snacks, and call it a night. I've really got to take some pictures, not only of the fractal cats but of myself as well. One of these days I'll get that camera I keep thinking about but never get around to purchasing. Until next time, take care, and keep fractaling forever. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_Peanuts { ; time=0:06:44.25 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+10.41462664889111000/+0.0473402357575368\
0/2.269743e+008/1/-2.5/-0.002
params=1/-11/-11/-1.1/0/5000 float=y maxiter=1600
bailout=25 inside=0 logmap=124 periodicity=10
colors=000<3>0000000000700600E90C40GB0JG0OM0RR<3>0do\
0hp0ir4ktBmtJpvRrxYtxfvzozzvzzzzz<2>zzzzzt<2>zodzk_z\
hX<3>zVCzR7zO3zK0tP0kU0dX0X_0Pc0Hh09k03o00r00v01m09f\
0H_3PU6YMBfEGo7Kx1Oz0Uz0Yz0az0Uz9KxOCoa4fo0Yh0Pc0HX0\
JR1PK1VG3a93f44m04r06x06v09v0Bv4CvBEvGHvKJvPKtXMtaOt\
fRtmUtrVtxXtzYfxGVt0Yo3ak4df7hc9i_BmVEpRGtMJxJKzGMzJ\
J<3>zPCzRBzU7<3>z_1za0zd0za0za1za1va3p_3k_4f_4a_6X_7\
RY7MY9HY9CYB7YBEX0KX06Y90_X0at0fr0ip6moEpmOtmYzk<2>z\
zfzzfzz_vzV<3>Yz9Rz4Kz0Gz09z03z00z00z00z00z70zH0xR<2\
>0xv3fkKkcckVvkMz_EzfHzcKz_OzXPzUUzPXzM_zJa<2>z9kz1m\
z0pz0tz0vzExzpxzrzztzxvzvxztzz<3>kzzizzhzz<2>czzfzpi\
zdmzUozO<3>vz9oz4iz1cz0Yz0Rz0Mz0Pz0Rz6VzGXzO_zYazhcz\
pYzkUzf<2>EzUBzO6zJ1zG<2>0z10z03z0Mz0dz0zz0zz0zzUzzz\
Uzo0zf0za1zY4zV7zPBzMEzJ0z0
}
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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