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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Do fractals exist on the astral plane? Of course. Fractals are everywhere, and on the astral plane they exist as real objective objects, not merely as mathematical abstractions. To prove my statement, I have found an image of an astral Minibrot, which I now present as the FOTD for October 8th. The expression that drew the image is -1Z^(-2)-3Z^(-4)+21*(1/C). It was entered totally at random. Of course, some may doubt that this midget originated in another dimension, but it is part of a four-dimensional Julibrot, and the fourth dimension most certainly is another dimension. The pale colors resemble the tints commonly reported as having been observed on the astral plane, and the deep blue background adds just the right heavenly touch. Taking all this evidence into consideration, I came to the conclusion that the midget in today's picture comes straight from a higher world. I named the image "An Astral Minibrot" accordingly, and rated it a marginally better than average 6. The parameter file runs in 8 minutes on a very down-to-earth physical computing machine. It will not run at all on an astral machine. If the 8-minute wait leads to too much impatience, the GIF file of the entire image may be found on the Usenet network at the binary newsgroup: The fractal weather today here at Fractal Central was partly cloudy with a temperature of 60F (15.5C). These conditions pleased the fractal cats, who were outdoors for nearly two hours, romping and resting. With another slow day, I once again had ample time to indulge in armchair philosophy. And once again the subject was the nature of reality, which is the most basic question of philosophy. I did a lot of vague pondering, obtaining no insights that I have not held for at least 20 years. Actually, the more I ponder the question of reality, the more I realize that I already know all that I shall ever know about the topic. Maybe I need a new topic to ponder when the urge to ponder strikes. Or maybe I need to do a bit less pondering. The nature of reality remains a mystery because we have no way of knowing how closely the sensory-produced images in our minds correspond to an exterior objective world, or even if a truly objective world exists at all. This is the situation. I have repeated it over and over for years now. Unfortunately, neither I nor anyone else has a solution to this mystery, which has existed ever since humanity developed the attribute of intelligent thought. Maybe it is an invented mystery, but regardless, I think it's time to devote my excess energies to the topic of fractals, and forget the pseudophilosophy until and unless I have some truly new ideas to offer. The cats are now dozing, and I'm about ready to doze myself. Until tomorrow, when the philosophical emphasis will be on fractal philosophy, take care, and be peaceful. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
An_Astral_Minibrot { ; time=0:07:59.23 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.5225568645555446/+0.311077241609439/4.\
203189e+009/1/97.499 params=-1/-2/-3/-4/20/0 float=y
maxiter=1400 inside=0 logmap=159 periodicity=10
colors=000DBFDDGBCJ<3>8CP7CR6CS6CV5CW4CY3C`2Ca2Bc2Ce\
0Bh0Ci<2>0Bm0Bn0Bm2El6FlAHkFIlJKiONgSOeWPe_QecSchVem\
WfsYfxagzdhzfjwiksiimjjfllYnmSpnMrpItrJvpKynLwmMtkNq\
jOnjPlhQigRheSedTabUZbVXaXU`YTZWPYWLXWJXYMYZPZ<2>eZc\
ghcimcircmmbmmbmh`lb`m``nW_pTYqOXsLWtHWuDUwATx7Ty4Sy\
1Sx5Tw9UuDUtHWsMWqQWpWXp__nbZneZniZnm`oq`pw`pzanwRns\
PnnOnkOnhNndLnaLnYKnWJnSJnQInPIpOHpNGpLGpLE<2>pICpGB\
pGBpEApEAj14l45l76l86lC6lE6mH7mL7mN7mP7mT7mV7nZ8nb8n\
d8ng8nk8pmApqApuAqxApzBpzBnzDkyEjwFhtGfqHdpI<3>YeNWb\
OVaPTZRRXRQURNSRMQSJPTHOWGLX<3>AEaFLcJQeNVfS`hXei`ij\
elffn`gqTktLnwEpy7rx9rwBswEruGttH<2>usOusRwsSwtVxuXx\
u_yu`yvcyvf<3>zypzyrzzuzzwxxuvxtrxsmypfym`ymVykQziKz\
hGzhAzgDzj<3>NzoPzqRzrUztWzv_zwazxdzy<2>kzzizrhzfczU\
bzH`z5VzQMzhDzzIzv<2>Wzc`zYczQgzJkzCnz7WzXNzHMzMJzT
}
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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