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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is part of the fractal that results when 1/Z is subtracted from Z before C is added. The parent fractal is little more than a hyperbola symmetrical to the X-axis, with the open end on the east side. In this case the 'main bay' is truly impressive. In fact, it is quite possibly infinite. But infinite or not, its shoreline is filled with typical Mandelbrot things such as buds and spirals. Today's image lies rather deep in one of the spirals. I gave the image the rather unpleasant name of "Spinal Tap" because the elements surrounding the central midget remind me of a spine, with its loosely connected discs and bones. Unfortunately for those in a hurry, the image is a very slow one. It takes over an hour to complete on my aged unit. The dark dreary colors add little to the image, and drag its value down to a 3. When the render time is figured in, the overall worth registers a shameful 4.7. But as in most all fairy tales, salvation is at hand. The task of rendering may be avoided. The finished image will soon be posted on the FOTD web site at: When I came to the end of the most recent outburst of philosophy, I had reached the point where I needed to decide between the philosophies of Positivism or Idealism. Positivism assumes that the world is really out there just as we observe it, and says that we can gain true knowledge about it by observing its phenomena and applying reason to our observations. Idealism assumes that the objects of our perception are actually interior mental images, which are all the mind knows directly, and not the exterior objects themselves, which we have no way of perceiving directly and which might or might not resemble the mental images we have of them. Being a person who enjoys fantasy, and aided by the scientific discovery that the conditions both down at the sub-atomic level and up at the cosmic level extend well beyond our limited commonsense world-view, I chose Idealism as my life philosophy, and the basis of solving the consciousness mysteries. This does not mean that I was ready to ignore the very successful scientific method of observation and experiment, but it does mean that I now considered the natural world that science investigates to be an assemblage of common and consistent mental images rather than a totally objective exterior reality. My view was strengthened by the near total failure of the scientific method when it is applied to things such as thought, emotion and consciousness, which is difficult to even define, and impossible to dis-assemble and analyze on a lab table. The problem was, and still is, that science works by taking objects apart and analyzing the pieces, while consciousness cannot be taken apart. The widely accepted scientific doctrine, (it is not a demonstrated fact), is that consciousness is somehow generated by the brain, in much the same manner as a transmitter generates radio waves. The basis for this doctrine appears to be that it must be true because there is no other known source for consciousness. But there is a hard problem with this view. The 'hard' problem, which so far has defied every attempt at solution, is to determine where the 'consciousness', whatever it might be, comes from. Science assumes there is nothing resembling consciousness in the sub-atomic particles and atoms that compose the material of the human body. Yet when these unconscious particles and energies are assembled into molecules and cells, and the cells start working together in the healthy brain, something absolutely new called consciousness emerges. The irony is that science is supposed to do away with the need for magic, and this view of self-awareness as an emergent phenomenon of the brain is a belief in magic of the highest order. When science studies things of the mind, the situation can become almost comical. When supposedly sensible scientists (or are they magicians) talk about things like the emotion known as love, they forget all about love and start discussing endorphins etc. But such chemicals are not the same as the inner feeling we know as love, and despite the endless parade of so-called new breakthroughs, no one knows how to change a chemical reaction into an emotion. Discussing brain chemicals when searching for the source of human emotion is as absurd as discussing the electrical currents in the circuitry of a television receiver when searching for the source of the program content. True, in both cases there is a connection, and the picture can be changed by tinkering with the circuitry, but the program does not originate in the circuitry. So now we find ourselves with two apparently unsolvable problems -- how can we exist when the probability of our individual existence is zero, and how does something as new and unexpected as consciousness arise from the activity of unconscious matter? I obviously have no scientific proof of the solutions that I have worked out, but I have found answers that, at least in my opinion, take away much of the mystery. We will take up from here in the next philofractal version of the FOTD. A cloudy cold day here at Fractal Central on Sunday, with a temperature of only 34F 1C, kept the duo safely indoors. When a few snowflakes started falling in the evening, they knew they had made the right decision. This morning is starting sunny but blustery, and even colder. I had best have the tuna ready again. As for the work, it is still a bit heavy, but I now have FOTD's in storage for the days when there is no time to do completely new ones. The next FOTD will appear on schedule right here in 24 hours or so. Until then, take care, and if you want to catch a squirrel, climb a tree and act like a nut. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Spinal_Tap { ; time=1:03:24.36--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+2.82715396322678/-0.00004849471454/1.6\
01449e+011/1/82.5/0 params=-1/-1/-1/1/0/0 float=y
maxiter=10000 inside=0 logmap=1152 periodicity=10
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zMKzNKzOKzPKzQKzRKzSKzTKz }
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.
