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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is a scene in the fractal that results when 8 parts of Z^(-11) are added to 12 negative parts of Z^(-1.1) before adding 1/C. Normally, this parent fractal would be an island surrounded by an infinite ocean, but by adding 1/C instead of C the entire fractal has been turned inside out, or inverted, and instead of appearing as an island, the fractal resembles a marshy area with X-axis symmetry, which is filled with debris-choked ponds. Perhaps the most prominent feature of this parent fractal is the large fan-shaped feature just east of the origin. Similar fan-shaped features often appear in inverted fractals created with negative powers of Z. At first glance, these fractal fans appear to be totally non-critical and therefore devoid of midgets, but a careful search sometimes proves otherwise. Today's image lies in the outskirts of a larger midget in a cut-off feature in the northern part of its parent's fan. I gave it the name "Curly Slices" when I noticed the resemblance of the four prominent features surrounding the midget to slices of bread with curly extensions attached to their top corners. Maybe it is just my less-than-cheery mood, but I could find nothing in the image that would rate higher than the slightly-below-average rating of 4 that I gave it. The 13-minute render time can be avoided by downloading the completed GIF image from one of the FOTD web sites, which may be found at: The Friday weather here at Fractal Central was very pleasant, and the cats were very happy. Warm sun, light breezes, and a temperature of 63F 17C gave them a comfortable afternoon in the yard. But this morning is cold and rainy, and it will likely stay this way all day, and the dynamic, sun-loving cats will likely be far less satisfied. For me it will be a day to finish a small amount of work and watch the rain. When I tire of watching the rain, I will turn to the world of fractals. The best fractal I find will appear as tomorrow's FOTD. Until then, take care, and turn to fractals when reason fails. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Curly_Slices { ; time=0:12:56.15--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+2.49903620056882100/+1.721148306093985\
00/1.123999e+010/1/63.5/-3.99690114282896802e-005
params=-12/-1.1/8/-11/0/525 float=y maxiter=1200
inside=0 logmap=261 periodicity=10
colors=000gbUgcTgcShdRieQjfOkgNlhMmiLnjKokIplHqmGr\
nFsoEuqDhjKWdQJYX6Sb5UY5WU4YQ4ZM6`P7aR8bU9cWAeZBf`\
CgbDheFjgGkjHllImnJoqKpsLqvMrxNszOruPqpPqkQpfQpaUr\
ZXsX_tVbuSfvQiwOlxLoyJrzHnwJjuKfrMbpNZnOVkQRiRNfTJ\
dUFdVE_WKgWFVWUUWHQUIOPJLKKJKLGKMEKNBKO9KPAKQAKRAS\
SAQTBPUBNVBLWBJXCIYCGZCE_CC`CBaADb9Ec8Fd6Ge5Hf4Ig5\
JhcJg6Kf6Ke7Kd7Lc7Lb8Lc8Mc9Mc9MdANdANdAN_BPXCRUDTQ\
DVNEXKFZHF_GHYGJWGLVGMTGORGQQGROGTMGVLGXJGYHG_GGaE\
GbD6j8Bk7Fl7Jm6Nm6Rn5Vo5Zp5bp4fq4jr3ns3rs3pr6or9nr\
ClrEkrHjrKhrNgrPfrSdrVcrYbr_`rb_reZrhYrjH`l0Kn4Jm7\
JlAJlDIkGIkKIjNHiQHiTHhWHhZNe`TcbYaec_ghYinWksUdrT\
YqSRqRKpQDpP6oO0oN4nM7nMBnLEmLImKLmKOlKSlJVlJZkIak\
IdkIejMfiPghSggVhgYif`iecjdfkcikclk`kkYkhalfdmcgma\
knZnnXqoVtoUunTvmSwlRxkQyjPziOzhNzgMzfLzeKzdJzcIzb\
HzaJz`Kz`Mz`Nz`Oz`Qz`Rz`Tz_Uz_Vz_Xz_Yz__z_`z_az_Vz\
aPzcIzeCzfMzj9zZCzYEzXHzV }
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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