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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's fractal, which pictures a midget in the land of Z^sqrt2+C, we slip back to a rating of 5. This perfectly average picture features a perfectly normal, though fractured, midget that exists in a remote valley of its parent fractal. I visit the Z^sqrt2 figure frequently because in this figure the midgets are relatively easy to find compared to the midgets in other figures with exponents of Z between 1 and 2. Since 1.4142 is the square root of 2, the midgets in the Z^1.4142 figure reveal their hiding places by being surrounded with the same two-way symmetry that reveals midgets in the classic Z^2+C figure. But in the Z^1.4142 figure the midgets lie far deeper and farther apart. I named the image "Blueberries" when I noticed the berry-like depressions surrounding the barely visible midget at the center. There are roughly 9 berries in the outer ring and roughly 13 berries in the smaller inner ring, which is not at all surprising, since 13/9 equals roughly 1.4142. The parameter file takes over 23 minutes to render on a 200mhz Pentium machine. It will run faster on a faster machine, but not so fast as to make a download of the GIF image file superfluous. That image file may be found on the Web at: The fractal weather today featured a steady rain from dawn to dusk. The temperature of 52F (11C) combined with the rain to keep the cats snug indoors in their beds. Once again we come to the end of the FOTD. It was a relatively brief one because I'm still busy. But eventually I'll catch up, and then, anything could happen. Until next time, take care, and help preserve fractals from extinction. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Blueberries { ; time=0:23:16.75--SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1
center-mag=-1.04105767849226400/-1.142969742678717\
00/1.290666e+007/1/90 params=1.414213562373/0/100/0
float=y maxiter=2800 inside=0
logmap=569 periodicity=10
colors=000GU0GU0ET0CQ0AO08M06K04I02G00D00D00B00900\
60050020020000000000000000000000000000000000000000\
0000000200200400400400600620640840860A80A80AA0CC0C\
E0CE0EG0EH0GH2GJ2GL2HL4HN4HP6JR6JR8LT8LVALVANXCNZC\
NZEP`EPbEPbCRdCRdATdATd8Vd8Vd6Vd6Xd4Xd4Ze2Ze2Ze0`e\
0`e0be0be0be0de0de0eg0eg0gg0gg0gg0ig0ig0kg0kg0kg0m\
i0mi0oi0oi0oi0qi0qi0si0si0uk0si0sg0qg0qe0oe0od0ob0\
mb0m`4k`6kZAiZCiXGiVHgVLgTNeTReRTeRXdP`dNbbNebLg`L\
k`Jm`HqZHsZGvXGxXEzVEzVCzVAzTAzT8zR8zR6zN4zR6zV8zX\
8z`AzbAzeCzgCzkEzmEzqGzsGzvHxxHvzJuzJszLszLozNmzNk\
zNizNgvNeuPdsPbqP`mPZkPXiPVgRTdRRbRP`RNZRNZTLXRJXR\
JXPHVPGYNG`NEcNEfLCiLAfJAcJ8_J6WI6SJ4PK4ML2JM0GN0D\
O0AP0AQ0AR0AS0AT0AU0AV0AW0CX0EY0GZ0G_0E`0Ga0Gb0Gc0\
Gd0He0Hf0Hg0Hh0Ji0Jj0Jk2Jl2Lm4Ln6Lo8Lp8NqANrCNsENt\
EPuGPvHPwJPxJRyLRzNRzPRzPTzRTzTTzVTzVVzXVzZVz`Vz`V\
zbTzdTzdTzeTzeTzgTzgRziRz
}
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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times.
