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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is a zoom into a curious image sent to me yesterday by Lee Skinner. I have named it "Illusory Minibrot" because of the deceiving nature of its symmetry. I rated it a 7 because in addition to its mathematical interest it is a striking image. A quick glance seems to show 32 filaments entering from the border of the image, but by the time the reddish teeth jutting into the blue area are reached, the symmetry has dropped to 16. Things are not as they appear however, for both of these apparent symmetries are false. The symmetry of the whole picture is one big illusion. Out beyond the 16 encircling yellowish arms, the actual symmetry is 8. Look closely at those 16 rusty-red teeth. They are not identical, but alternate between two different varieties, making the complete circle consist of 8 groups of 2. The smaller teeth have one long filament attached, while the larger teeth have 3, giving a total of 32 filaments extending out beyond the image border. The reason for this pseudo-symmetry is not altogether clear, though it is certainly connected to the periodicity of the area and perhaps to the value of the exponents of the generating formula. Regardless, it is a promising area to investigate, which I will likely be exploring in the not-too-distant future. The image takes 18 minutes to render on my machine, which is an old-style Pentium running at 200mhz. Within an hour or two, the file of the completed GIF image will be posted to: The fractal weather today featured clouds, light rain, and a most un-summer like temperature of 64F 18C. The cats complained a bit, then went to sleep. I notice that the cats are romping less and sleeping more as the months and years pass. They must be starting to feel their age. As for myself, I'm feeling the need to get some work done. So until next time, take care, and don't write off the Philofractal list as dead yet. I've got a lot of controversial stuff yet to discuss. All I need is the time to sit down and write it. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Illusory_Minibrot { ; time=0:18:34.17--SF5 on a p200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-4.28968168524079100/+0.751079008850680\
90/1.517355e+012/0.9996/-175.008/-0.043
params=0.05/4/0.01/5/0/0 float=y maxiter=1800
inside=0 logmap=373 periodicity=10
colors=000M6FL4EK2CJ0BI1DI1EH2FH2GG2HG3IF3JF3KE4LE\
4MD4ND5OC5PC5QB6RB6SA6UA7V97W98W89X8AY7BZ7CZ6D_6E`\
5Fa5Gb4Hd4If3Jh3Kj2Kl2Kn2Kp2Kr1Kt1Ku1Kv1KwF0hk0ak0\
Uk0Nk0Lk0KmKJkPIiUGhZFg`EfcDdfBahA`k9Zm8Xp6Vr5Tu4S\
w3Rv4Qv5Qv6Pv6Pv7Ov8Ov9Nv9NvAMvBMvCLvCLvDKvEJuFJsF\
IqGIoHHmIHkIGkJGlKFmLFnLEoMKpNPqOUrOZtPcuPhvQmvQrw\
QwxRzzRrySmwShxScxTZxTUxUPyUQyUTyVTyVTyWTzWSzWTzXU\
zXUzXSxWQvWOtVMrVKpUInUGlTEjTChSAfS8dR6bR7eU7gX7i_\
8kb8me8ph8rk9tn9vq9xt9zwCwsEtpHqlJniMleOibRfZTcWW`\
SYZP`WLbTIeQEgOBiREjTGkWJlYLm`OnbQoeTpgVqjYrl_sobt\
qdusftmgshhrciqZjpUjoOknJlmEml9nl4ni9pfEqcJsaOtZTv\
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USOQQTLPYHNbCMg8SiCXkFamJfoMkqQpkTxANqEOkHPdIUZJZS\
KcMLhFMm9NrFOwLPzQQzWRz`SzfTzkUziWzhXzfYze_zcazbcz\
aez_gzZizXkzWmzUmzTmzSmzPmzNmzKmzImzJmzJmzJmzJmzJm\
zKmzKmzKmzKmzKmzLmzLmzOmz
}
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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times.
