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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's piece of fractal art is a tiny part of the fractal that results when Z^(1.25) is subtracted from Z^(-0.75) before (1/C) is added. The parent fractal consists of two small Mandeloids surrounded by considerable fractal debris. Today's scene lies in the East Valley of the smaller Mandeloid. I named the image "Happy Anniversary". The name was whimsical. I have no anniversary that falls on January 14th. But the name is entirely appropriate, for the odds are likely that someone who reads this message will have some kind of anniversary on January 14th. When rendering the image, I set the outside to 'summ'. The result was an image worth a rating of 7. When the render time of over 12 minutes is taken into consideration, the overall worth registers a respectful 57. For convenience, the finished GIF image is posted on the FOTD web site at: At the end of the most recent FOTD philosophical ramblings, I had reached the point where I had become fascinated by the curious similarity between the microscopic world within the atom as described by quantum theorists and the many vast worlds of existence as described by mystics. Considering that science rejects mystical inner experience as a way to knowledge in favor of objective repeatable scientific experiments, this similarity seemed strange. And the similarity is striking indeed. Both quantum scientists and enlightened mystics tell us that the truth is so far removed from the intuitive world of everyday experience that it cannot be expressed in words. I wondered whether this similarity could be a total coincidence. If so, it is most awkward for the scientists, for it puts them in the unenviable position of needing to spin off ever more explanations to convince the unscientific public that the similarity is nothing more than a coincidence, and that the near-mystical conditions scientists tell us exist at the sub-atomic level have no effect on the world of everyday experience. The scientists see the quantum as an unfortunate discovery which, due to questionable popularization, the public sees as giving validity to claims of the paranormal and the supernatural. All the while, the mystics simply relax, continue meditating, and tell us that science is merely discovering the things that mystics have known and taught for thousands of years. The continued popularity of 'new-age' beliefs shows that the public remains unconvinced by the scientists' spin. The scientists cannot be blamed for their effort to minimize the metaphysical implications of quantum mechanics however. Q.M. places the universality of the philosophy of positivism into question, and science bases its validity on the ability of the physical senses to reveal truth. The intensity with which 'skeptics' and 'believers' debate the meaning of the quantum puzzles and the existence of the paranormal is a sign that religious-type faith is involved on both sides. True believers are convinced that supernatural things actually do exist, and defend their view vehemently. They cling to their view largely because, if the supernatural is true, then survival of death, which gives their lives meaning, is more likely to be true. Skeptics are just as vehement in defending their view that science will eventually find a natural explanation for every mysterious phenomenon. They cling to their view largely because to them the perceived reality of the physical world serves as a solid foundation for their world view, and fills the role once filled by the image of God. To me, these two views seemed extreme. I was convinced that the truth must lie somewhere in between, or perhaps in a blending. To be continued in the next philofractal FOTD. . . . A damp, mostly cloudy day with light sprinkles on Thursday kept the fractal cats close to the house, but the temperature of 63F 17C lured them briefly into the thicket, where they managed a 10-meter journey. This adventure kept them as happy as old codger cats can be. Today is starting with heavy rain and flooding. It is also turning colder. The day will hold hazards for the dynamic duo. For me, it's work then fractal fun. The next FOTD will appear right here in three days on January 17. After that, it should be back to the daily FOTD schedule. Until then, take care, and be serene. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Happy_Anniversary { ; time=0:12:22.22--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.36380452105611450/-0.077315904189054\
44/1.587035e+009/1/92.5/6.30355824760009398e-007
params=-1/1.25/1/-0.75/0/0 float=y maxiter=2000
inside=0 outside=summ logmap=265 periodicity=10
colors=0000A00E00I02M07Q0AU0EW0IY0M_0Oa0Pc0Pe2RgAR\
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GzwEztAzr8zn7zm2zi0zg0zd0zb4zYCzVrz8tz0vz0wz0nz0gz\
0`z0Tz0Mz0Ez08z04z00z00z0 }
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 PARAMETER FILE=========================================
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times.
