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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For some strange reason, today's fractal image reminds me of a specimen on a microscope slide, giving me more than enough reason to name the picture "Mandelbrot Specimen". The rating of 7 may be a bit liberal, but with its striking hazy blue atmosphere, the image is definitely at least a little above average. The iterated formula adds a tiny bit of Z^(-141.42) to a far larger portion of Z^(-1.4142) before adding (1/C). The resulting teardrop-shaped parent fractal at first appears to have x-axis symmetry. This apparent symmetry is an illusion. At greater depths, the positive and negative halves are entirely different. The most obvious critical area of the teardrop is at the blunt east end. But today's scene lies not in the most obvious main arm, but rather deep in a tiny hole in a minor lobe just north of the main arm. The sharper west end of the parent fractal also has interesting areas, which I have not yet touched and may never touch. After all, I've got an infinity of other infinite fractals to explore and not quite an eternity in which to explore them. The 1-1/2 minute render time of the parameter file is reasonable enough for today's relatively easy image. For those with more patience, the GIF image file will be posted in 16 hours to Usenet at: The fractal weather today was cold, cloudy, foggy and drizzly. Combined with a temperature of 43F (6F), it kept the fractal cats indoors snug in their beds by the radiator. The following material could be considered depressing. Readers who do not wish to be depressed should stop reading now. I actually did do a bit of philosophizing today, comparing the ancient mystical view of the world with the modern scientific view. The ancients considered the world to be like a tower, with level upon level of spiritual levels extending above the physical ground level, all the way to the highest heaven, where presumably God dwells. Man was considered to have, or more accurately, to be an immortal, indestructible spirit, which would drop the body at death to begin existence on the higher planes. Since the human spirit was supposed to exist forever, men, at least good men, would have the opportunity to observe and experience all there is to experience on every higher level that exists. The ancients believed that after death man could experience the things he can only think and dream about in this life. It was a good world view while it lasted, but it had its flaws, most notably the total inability of the higher levels to be detected. Then man developed the scientific method, and gradually the mystical view of the world was replaced by the modern scientific view. In the scientific view, the tower of spiritual levels is gone. Only the plain of the physical ground level remains, but this ground level has been expanded to beyond infinity. The world is still of infinite extent, though the expanse is now horizontal rather than vertical. The spiritual distances above have been transformed into the material distances out there. The wonders of the world as seen by modern science exceed the wildest dreams of ancient man, but now he is told he will never have the enjoyment of observing and experiencing those wonders. In his limited time and with his physical frailty, a single man cannot observe or experience even 1/100th of 1 percent of his home planet, not to mention the countless planets, stars and yet-to-be-discovered things that exist in the universe. Man, as science sees him, can do nothing but reflect briefly about the wonders that might exist in the vastness of space, then die and cease to exist with not the slightest chance of experiencing those wonders. To those who believe, religion offers hope that such a bleak outlook can be avoided. It is a consoling thought, but most scientists, though they do not often speak it openly, consider religion to be not much more than a holdover from the childhood of humanity, an outdated delusion that is now doing more harm than good. And when science and religion are in conflict, science inevitably wins. Apparently the ineluctable harshness of reality can not be escaped. These are the kind of thoughts I think when I ponder. As I close today's discussion with these Atheistic thoughts, things are looking bad indeed. Is there a way out that does not involve wishful thinking? Simply because we would wish a thing to be true does not make it true. Must we delude ourselves to find peace of mind? Must we grit our teeth bravely and try to find peace and meaning within the limits of our physical existence. Or must we live out our lives in a state of quiet despair, trying to convince ourselves that this despair is happiness? I'll have more cheerful things to say on this topic in a FOTD discussion in a few days. For now I see it's time to shutter-up the fractal shoppe and call it a night. Until next time, take care, and fractals make life wonderful. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
MandelbrotSpecimen { ; time=0:01:23.77 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+2.413788574630565/+0.191409102126881/3.2\
20006e+011/1/-87.501/0.001 params=100/-1.4142/1/-141\
.42/-0.98/300 float=y maxiter=272 inside=0 logmap=18
symmetry=none periodicity=10
colors=000Cef<3>HTaIQ`05KKKZ05KMEXWVcirorzzzuwlgt<2>\
jHyj8zgAx<6>THjRIhOJf<2>IM`GN_FMY<6>BLPBLOALM<3>8LH8\
LQ7WS7YUD`W<2>ULa_KceLejMgiNi<3>fSteTweUz<2>cXz<3>N`\
zIazEbzAcz6dzXez<3>zhz<7>jhz<4>`hz<5>khzmhzohz<3>vhz\
<3>Ghz<5>UhzXhzZhz<3>ghz<3>0hz<6>HhzKhzMhz<3>Vhz<3>J\
hzHhzNhz<3>ghz<3>PhzLhzGhz<2>3hz<2>Khz<9>DhzChzBhz\
<3>9hz<7>ahzehzhhz<3>vhz<4>whzwhzwhz<3>whz<8>chzahzZ\
hz<3>Rhz<3>ehzhhzlhz<2>vhz<2>Fhz<3>`hzehzjhzFhzahzxh\
z<3>PhzHhzIhz<3>LhzMhzMhz<2>qhz<2>ihz
}
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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