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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Start with a bit of 1/Z, add a lot of Z^100, then add 1/C and iterate a few thousand times. What do you get? -- a fractal of course. The fractal, which is not visible in its entirety unless an out-zoom is done, consists of a central Mandel-like figure, with two vaguely Mandel-shaped satellite objects located symmetrically north and south of it. Today's little midget is located in what passes for an East Valley of the north satellite. Actually, today's midget is in the northeast suburbs of a larger midget in the pseudo-East Valley of the north satellite. I named the picture "Quadrilateral" when I noticed that most of the elements seem to be in the shape of four-sided geometrical figures. The rating of 6, which is a bit above average, seems an honest assessment of this unassuming image. I was surprised when I saw the difference made by adding such a small portion of 1/Z to the Z^100 fractal, which is basically a circle. But the most unlikely things seem to happen in the world of fractals. If the portions of 1/Z and Z^100 are reversed, real(p3) needs to be reset to -0.99, but when this is done, another interesting fractal results. Tomorrow's FOTD will be a scene in the fractal that is the reciprocal of today's. With a render time of just under 20 minutes, the slow parameter file demands a trip to one of the FOTD web sites for a download of the GIF image file. Those sites are found at the URL's: The fractal weather today was once again perfect. The temperature of 86F (30C) and clear skies kept the cats happy. And in addition to fractals, happy cats are one of life's greatest enjoyments. It's now getting late and near the time to shut down the fractal shoppe and call it a night. OK, it's a night! Until tomorrow, take care, and never forget that it's easier to think of questions than to give answers. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Quadrilateral { ; time=0:19:18.54--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-8.6414574311906/+4.74639557029845/4.67\
691e+008/1/-82.503/0.001 params=1/-1/100/100/-0.1/0
float=y maxiter=3300 inside=0
logmap=393 periodicity=10
colors=000MLOMLOGOP9SJ3YE0b80h30m00n00n00n01p04p09\
p0Cq0Hq0Kq0Ns0Ss0Vs0Yu0bu0eu0iv0mv0pv0ux0xx0zu0zx0\
uy1nz4hz6bz9XzCQzGKzHEzK8zN3zP4zN6zM6zM8zK8zK9yJ9v\
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0zb3x`8v`Cs`Hq`Mn`Qm`Vk`_h`cf`hc`mb`n``q``fcfeTfeJ\
fc8fc3fc0fe0hf1hf4ih6ii8iiBkkCkmEmmHmnJmpKnpNnqPps\
QpsTpuVqvXqv_sx`sybsyeuzfuzhvzhuyhsxhsvhquhpshpqhn\
phmnhmnhkmhikhiihhhhffhfehechcbhc`hbeiY`hbYfeTdhQa\
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0az6XzBPzGPzMKzQKzVKz`AzeKziUzpczumzymzzmzzmzzmzqc\
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nBNp9Nq8Ns4Nu3Pv1Px0Px0Px0Px0bx6pxJzxVzxfzxezxczxb\
zx`zx_yxYvxXsxXpxVmxTixSfxQcxP`xNYxMVxMTxNTxNTxNYx\
SbxXex`ixemxiqxnixncxiYxc
}
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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