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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I see mentioned on the list the question of whether the incredible increase in computer speed and efficiency can continue. I say yes, for good or for bad, the speed increase will continue for some time yet. The only ultimate limit I can see is the speed of light. Signals cannot flow through the circuits faster than light. This limit can be made less significant by continuing to reduce the size of the computing parts, but ultimately, unless we turn to something entirely new, such as quantum computing, computers will reach an insurmountable limit. One drawback to miniaturization or quantum computing is that as the size of computing units decreases, the machines will become ever more fragile and subject to disruption by normally insignificant things such as cosmic rays. Perhaps more important is the fragility and complexity of our stored data. How long a computer disk will endure is one problem. A greater problem will be our ability to decipher the stored data when the machines and programs that created that data are lost. I doubt that any species, however intelligent, would be able to make sense of a computer disk containing a Pagemaker file if they had no clue to the type of machine that could read it and no knowledge of the Pagemaker program. As I grow older and ever more cynical, I begin to see the current explosion of population and technology as being out-of-control, almost pathological. I recall the passenger pigeon. 200 years ago, 10,000,000,000 of these dove-like birds filled our North American skies in perhaps the greatest bird-population explosion of all time. Today their number is zero. They are gone because they became over-specialized, needing exactly the right conditions to reproduce. When the intrusion of man altered those conditions, the birds could no longer reproduce, and were extinct in less than 100 years. Just like the passenger pigeon, the human population is in the midst of a similar population explosion, and also developing the need for ever more specialized conditions to maintain its advanced civilization. What would happen to us if we somehow lost the use of the computers that we depend on to maintain our way of life? There are many ways this could happen. I have long since given up hope that man will one day reach the stars. I now have doubts that he will reach even the planet Mars. And it is by no means certain that 200 years from now there will be men to wonder what went wrong. But men still exist today, and fractals will always exist, and it is now time to turn to fractals. To produce today's fractal, I took most of the 1's in the formula of yesterday's fractal and changed them to 2's. I had no mathematical reason for doing this, I did it only for fun. (I could not simply change the 1's in yesterday's real(p3) parameter to 2's because doing so would have produced an inferior fractal.) When all the number-changing was finished, I had created another oversized area of chaos, this one with its main Mandeloid well beyond the borders of the default screen. This Mandeloid resembles a nearly perfect M-set. Today's scene is located in one of the rays radiating from a larger midget, which lies just beyond the tip of the main stem of the large Mandeloid. Thanks mostly to the strong coloring, the image rates a 7. I named the image "Two Satellites" when I noticed the two prominent areas in the corners of the image, which obviously hold still smaller midgets that are beyond resolution. The render time of 7 minutes is fast enough, but downloading the finished GIF image from: Thursday was an exceptional day here at Fractal Central. How often does a day come in the middle of winter, with almost hot sunshine and a temperature of 63F 17C? . . . Once every two or three years? The dynamic cats took advantage of the unusual conditions by spending almost the entire afternoon in the yard, trying to ignore the remaining puddles and mud. Needless to say, their moods were as exceptional as the weather. Today is starting sunny but colder. It will be harder for the dynamic ones to stay happy, but they are already eager to get outside and give it a try. And as always, I have a few tasks to finish, so until next FOTD, take care, and I wonder where I could find a projective plane. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Two_Satellites { ; time=0:07:21.10--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-7.38358917092518/+20.54585830913693/6.\
4431e+009/1/-122.5/-0.00244863563439755294
params=2/2.2/-2/-2.22/-1.3/0 float=y maxiter=1200
inside=0 logmap=157 periodicity=10
colors=000D9AC0FA3L99P7FT6L_4Qc3Vg1`l0fr0lv0rz0vz0\
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LAzICzFDzAFz7Gz4Iz1Jz0Gz4 }
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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