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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's fractal we continue the one-step-a-day climb to the fractal heights. Perhaps with a bit of exaggeration, I rated today's image a 7. The scene exists in a remote (but not too remote) part of the infinite logarithmic spiral that is the fractal created by the simple formula Z^1.43+C. All fractals in this range are filled with discontinuities -- branch cuts if that's what you would call them. These breaks frequently spoil an image by cutting right through the most interesting part of it, but sometimes the breaks become so pervasive that they form their own patterns. Today's image consists entirely of such fractal bits and pieces. I named the picture "Ignacio". Once again I cannot justify my choice -- I simply like the sound of the word. As is the case in most of my fractals, a minibrot lies at the center of the screen. This midget is typical of midgets when the exponent of Z in the generating formula is in the range of 1.43. The midget is immediately identifiable as a minibrot, but its shape is distorted almost beyond recognition. The scene is filled with smaller midgets, one of which sits on the longest filament. If this smaller midget is interesting, I might pull it up and declare it FOTD in a coming post. The color palette of today's image features a cloud of fiery foreground fragments floating before a hazy blue background. The draw time of the parameter file is 6-3/4 minutes on an aging Pentium 200mhz machine. As is always the case, the GIF image file can be downloaded in one minute or so from the Usenet binary newsgroup: The day's weather featured lots of clouds, a raw wind, and a temperature of 54F (12C) -- unpleasant enough to keep the fractal cats snugly indoors, wishing they could be comfortable out in the yard. And I wish I could find that philosophical muse, which seems to have deserted me. I'll try to philosophize tomorrow. If I fail, I'll still have a fractal. Check then to see what happens. Until next time, take care, and see you soon. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Ignacio { ; time=0:06:45.50 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1 center-mag=+0.3055\
2729081659520/+1.59327449871295100/1983.157/1/175
params=1.43/0/-0.47/0 float=y maxiter=30000 inside=0
logmap=95 symmetry=none periodicity=10
colors=000zUHzUGzRGzPG<3>wGGwEGvEG<3>qDGpDGpCFoCFmCF\
lCFkAFjAFhAF<4>d8Fc8Fa8F<3>Z7EY7EW6E<2>U5ET5ER5EQ5EP\
3EO3EN3EL3EL2C<3>H1FG1GE1HE0I<3>90K80K70L00D20G50I70\
M91PC2RE3VH6XJ7Z<2>QChTDkVGmYHp_IscIwaJu<4>aKuaKt`Kt\
<2>`Lt`Lt`Ns<8>_PrZPrZPrZQp<4>ZRpYRoYRoYTo<3>YUnYUnW\
Un<3>WVmWVmWWmVWmVWnVWoVYpVYrVYsVYt<3>QTyPRzOQz<4>IK\
zHJzGIzEHzDGz9EzADzCEzDEzEGz<3>JHzKIzLIz<3>RKzTKzULz\
VLzWNy<3>`OxaPwcPwdQueQufQugRthTtjUt<3>mZtm_to`t<3>r\
essfsugs<3>xlsxmsyos<2>zrsworrkrogpjdpf`oaYoZUnUQnQN\
mLJmIGlDCl21b98lECuGEwHHxIIyJKzKLzLOzNPzORzPUzQVzRYz\
TZzU`zVazWdzVfzWezWdzWczYazY`zY_zmLzmLzoKz<5>sJzsJzu\
Jz<4>xIzxIzyIz<4>zHz
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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