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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's fractal wonder, we turn once again to the MandelbrotBC formula, which works wonders with Mandeloids of fractional orders. I'll be using this formula often in the days to come, but unfortunately I have lost track of the formula's author. I believe the author is Andrew Coppin, though I'm not sure. Perhaps the author will claim his authorship. I noticed a flurry of mail on the Fractal-Art list when I opened my virtual mailbox this afternoon. The flap appears to be about another case of fractal thievery. It appears that someone was caught with someone else's fractals on their web page, and might be making money from fractals that are not theirs. Of all the things I have to worry about, copyright infringement is pretty far down the list. Maybe my lack of concern is because I feel that my fractals are not worth stealing. After all, they're only one-layered 256-color images of midgets, in a world of more colors than the eye can distinguish, and multiple layers piled on top of one another. Actually, I simply accept that my images and discussion might be stolen. If they are stolen and used for profit, and I don't know about it, I'll have nothing to get upset about. I have no time to worry about all the things that might be happening that I don't know about. If I find out about blatant profiteering from my work, then I'll know what to do and who to do it to. The mere act of posting something on the internet makes it available to anyone in the world with an online computer. And it's nearly impossible to prevent thievery. It's the artistic quandary. We want as many as possible to admire our work, yet we don't want the admirers to admire it so much that they steal it and make more money from our work than we make ourselves. While I'm trying to think of a solution to this unsolvable problem, I'll draw attention to today's FOTD, which I have named "Fractured Fractal", and which I have rated a respectable 6. The name arises from the fractured nature of the elements surrounding the mis-shapen midget. The iterated expression behind the image is Z^(2.05)+C. I have used the MandelbrotBC formula to draw a remote part of the infinite fractal created by this expression, a part that is quite chaotic and filled with almost-but-not-quite perfect midgets. The attached parameter file is slow -- 20 minutes slow. A download of the GIF image file is fast. I leave it up to the reader to decide which way to go. If they decide to take the download, the image file will be posted shortly to: The fractal weather today was partly cloudy breezy and chilly, with a sunshine shower of small hail just before sunset. The temperature of 46F (8C) permitted the fractal cats only 15 minutes out of doors, leaving them testy. Well, I see it's time to shut down. I'm just starting to get things back into their familiar state of dis-organization, and I want to do a bit more of my style of organizing before I totally run out of steam. Until tomorrow, take care, and exist in peace. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractured_Fractal { ; time=0:20:05.34--SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotBC passes=1
center-mag=+1.35355495637857600/-0.015397043802760\
70/475604.2/1/-52.499 params=2.05/0/56/0 float=y
maxiter=5000 inside=0 logmap=295 periodicity=10
colors=000olLQfJPdJPcIOaIM`GL_GJYFIXFIVDGTDFSCDQCC\
PAAOAAM99L97J76I74G63F64D33D63D73DA3DC3DF1DG1DJ1DL\
1DO1DP1DS0DT0DX0DY0D`0Da0Dd0Df0Di0Dj0Dm0Do0Dr0Ds0D\
v0Dx0Dz0Fz0Dz0Dy0Cx0Cu0As0Ap09o09l09i07g07d06c06`0\
4_04X04V03S03P01O01L00J00G00F00C009007004003000000\
0000000000000000100410630960A70D90GC0ID0LF0MG0PJ0S\
L0TM0XP0YQ0`S0cV1dX1gY1i_1lY1mV1oT7rQFsOMvMTxJ`zId\
zFizDmzArz9vz6vz4vz7rz9ozAvzCzzDzzFzzGzxIzvJzuMzsO\
zrPvpQyoSzlTzjVziXzgYzf`zdavccoadg_f`YgXXiYVj_Tl`S\
oaQpcOrdMsfLugJviIxjGylFzjFzlDzlCylAvmAslArlCplCol\
DmlDllFjjGijIgjJfjLdjMcjOajPajQajSaiQaiPagOagMagJa\
fIafGadFadDadAcc9cc7ca6ca3ca1c`0c`0c_0c_0c_0cY0cY0\
cX0dY0c_0c_0c`0ca0aa0ac0ac0ad0af0`f0`g0`g0`i0_j0_j\
0_l0_l0_m0Yo0Yo0Yp0Yp0Yr0Xs0as0fu0jv0ov0sx1xx1zy1z\
z3zz3zz3zz3zz4zz4zz4zz6zz6zz6zz7zz7zz7zz7zz7zz9zzA\
zzAzzCzzDzzDzzFzzFzzGzzIz
}
frm:MandelbrotBC = { ; formula written by ? ?
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.
