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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's scene we return to the most important fractal of all, the Mandelbrot set, to check the north branch of the valley of the large period-5 bud on the northwest shore of the main bay. We wander quite deep into one of the seahorse spirals on the outside of the valley, though at this point of the M-set I am undecided whether the spirals are more like seahorse tails or elephant trunks. We end up at a rather routine midget. The midget itself is nothing that has not been seen many times before, and by itself would rate a 5. The extra brilliant coloring however raises the rating to a 6. When the render time of one minute is taken into consideration, the overall worth equals a resounding 559. The magnitude of the image is right on the border of arbitrary precision math. When the image is rendered with conventional math, it finishes in one minute. When arbitrary precision math is used, the image drags on for an hour. The difference in appearance between the images drawn by the two rendering methods is very small, so I have inserted the mathtolerance entry into the included parameter file to insure that the very speedy conventional math is used. I named the image "Fractal Delicacy". At this depth, the spirals are delicate indeed, and do not quite resemble anything in the 'real' world. Thr best way to see the delicacy is to run the parameter file. Those with machines that fight the program may wish to download the image from the FOTD web site at: In the most recent outburst of philosophy I told of how I started to become disillusioned with Atheism. I had tried for several years to be a good Atheist, to convince myself that there is no God, that everything which exists is a part of the familiar world we observe with our senses and instruments, and that nothing exists beyond the things that might ultimately be observed with perfect physical instruments. But at heart, I am, and always have been, an Idealist. And, as dis-satisfied as an Idealist might be with conventional religion, it is hard for him to be an Atheist. How could I be so certain that there is no God when I had no concept of the thing I was denying? How could I be so certain that my conscious existence would end at death when the very phrase 'after death' had been shown by Einstein in his theory of relativity to be ambiguous. I might have been a successful Agnostic Freethinker in the 19th Century, but I had little chance of making it as an Atheist in the latter part of the 20th Century. Things became worse a few years later, when I became interested in Quantum Mechanics. In my youth, I had read a story about a man who starts shrinking, and continues shrinking until he discovers that the things we call atoms are actually entire galaxies, with stars and planets like our own. That story had started me wondering what I would actually see if I were to shrink down to the size of an atom. I hoped that quantum mechanics would give me the answer. But instead of an answer I found only more confusion. To start, I found that to properly understand the theory of Q.M. one needs a greater knowledge of mathematics than I possessed. The theory is basically a set of mathematical expressions and equations that happen to work quite well. No one, not even those who developed the theory, seems to know exactly what those numbers mean. There are many interpretations of the meaning of Q.M., but all of them involve something that defies common sense, and a person is free to choose the interpretation that he feels most comfortable with and that works best with the problem at hand. But all interpretations of Q.M. are no more than cleverly worked out models that try to reduce the Q.M. math expressions and formulas as closely as possible to intuitive ideas that we can rationally work with in our minds. So it turned out that I would never know what a bare atom looks like because an atom is a model, an idea invented by men, and in itself does not possess the attribute we know as appearance. And even worse, it seemed very possible that the sub-atomic particles which compose atoms might not even exist as objective realities. Sub-atomic reality is one of the common-sense things that some interpretations of Q.M. force us to surrender. Actual sub-atomic particles might be no more real than the observations we make of them. In a way, it appeared to me that our world might be made of atoms that can never be directly observed and are made of things that exist as real objects only in the mind. This is not exactly true, but, as an Idealist, I found the possibility fascinating and had no trouble using it as a source for further thought. Around this time I picked up a book titled 'The Tao of Physics', which points out how closely the world view of modern physicists resembles the things that Eastern mystics have been teaching for thousands of years. This book opened a whole new field of philosophical thought. . . . To be continued in a few days in the next philofractal FOTD discussion. The fractal weather was questionable on Sunday here at Fractal Central. We had many clouds, a little sun, some wind, but no rain. The temperature of 48F 9C made conditions acceptable to the fractal cats, who spent several hours on the porch, hoping for an occasional shaft of sunlight to filter through to the porch, and several more hours clearing the holly thicket of stray cats. Actually, Tippy did the clearing. He is the tough, wiry tabby. Thomas, the lazy, oversized yellow-orange one, just sat there and watched the intruder dash away up the hill to where he belongs. This morning is starting pleasant enough. The duo should have another good day. My day will be good when I have the work under control. From the way things are going, the next FOTD will appear in 3 or 4 days, when, if nothing unexpected happens, I should have a full week of nearly complete FOTD's on file and ready to go, enabling me to resume the regular daily schedule. So until late in the week, take care, and as you go through life, wonder about your trip. Jim Muth jamth@mindspring.com jimmuth@aol.com |
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