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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I named today's fractal "Ferndale". I gave it that name not because the image contains anything like a fern, and not in honor of any town of that name, but because the word just came to mind while I was studying the image trying to decide what to name it. The iterated formula is 10Z^(-10)+Z+(1/C). Such a formula would not be expected to make much of a fractal . . . well, maybe that's no longer true, since I've been making quite a few interesting fractal images with such formulae lately. The image, which rates a 6, features the standard midget at the center, surrounded by a pink and turquoise pattern of dark and light spots arranged in inwardly spiralling arms. The GIF image was souped up in a graphic program to give it a little added zip before I posted it to: The parameter file renders in 2 minutes or so, making it a toss-up as to which way of viewing the image is the more efficient. The fractal weather was once again perfect, with deep blue skies, low humidity, and a temperature of 82F (28C), which was perfect for cats. Unfortunately, when the fractal cats went outdoors, they were harassed most of the afternoon by a blue jay, who must have thought they were after its babies. But those angel cats would never harm the bird -- they just want to eat the birds. My philosophical musing returned to my old favorite, the abstraction of the fourth dimension, this afternoon. I tried for a few minutes to visualize double revolution and a surface of double revolution. I failed miserably. But even though I failed to visualize this four-dimensional object, that does not stop me from thinking about it. I may ponder the imponderable again tomorrow, but regardless of the outcome, I'll have the next fractal ready. Until then, take care, and the formula for the hypervolume of a five-dimensional hypersphere is 8/15*PI^2*r^5. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Ferndale { ; time=0:02:12.42 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip
passes=1
center-mag=-3.15202487684002900/+1.00536788746322700\
/6611.272/1/-25 params=1/1/10/-10/0.15/0 float=y
maxiter=1200 inside=0 logmap=27 periodicity=10
colors=000000CDE<5>IJK<3>MNOOOPQPQ<3>YTU_UVbVW<2>kYZ\
nZ_q_ZtbZwd_zdZwd_t`YqXVrTS<2>uJIvGFwDA<2>u40t10s00r\
00f16XAMLKaAUrTcz0hz6mzAcxFUsJToOXjSYfX`cac_fdV<2>sl\
IxoDzpAxlDsgFocIj_JfVM<3>PDVL9XG3XI4YI4YI4_I4_I6`<2>\
J6aJ7aJ7cJ7cL7cL9dL9dL9fL9fL9fJ9iGAlFAmCCpACr7Du19y6\
DvAGuFJsIMrMQpQToVXlY_jaaiffgjifmldroavr`zv_zyY<2>zz\
TzzSzzSzzSzzQzzQ<2>xzPuzPsyPpyPozOlzOjzOpzD<3>OzrGzz\
9zzAzzCzzCzzDzzFzzFzzGzzIzzIzzJzzLzyLzxMzvOzuOzsPzsQ\
zrQzpSzoTzmTzlVzjXziXziYzg_zf<2>azaaz`cz__zVcz_gzalz\
f<2>yzpzzszzxzzvzzuxzs<5>YzjTziPzg<3>7zaCzc<3>OziSzj\
Vzj<3>gzpjzrmzspzsszuxzvzzxzzy<2>zzzzzzzzyzzvzzu<2>x\
zmuzjrzgozfmzcjz`gz_fzXczT`zSYzPXzMTzLQzIPzFMzDJzAGz\
7Fz6Cz39z00z07z0<2>Yz1fz1oz3xz3CzQ7zO4zM1zJ0zI0zF
}
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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