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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: As my mood lightens, the fractals are coming easier. Today's fractal for example took me all of 5 minutes to find and all of 50 seconds to render. The iterated formula subtracts Z^(-1.1) from Z^(-0.9). The tiny difference is then multiplied by a factor of -548.998 before adding 1/C. The real(p3) parameter is extremely critical, the slightest change resulting in a totally different image. The midget at the center of the image is actually located on the negative stem of the tiny M-set that forms the parent fractal. (Since the stem points east, I guess it's a positive stem.) The sparkling features surrounding the midget remind me of dewdrops on a spider web. These dewdrops inspired the descriptive but not very poetic name "Midget with Dewdrops". The picture seems just a bit above average as FOTD's go, and as a result has been given a rating of 6. An additional good point of the image is its speed. The parameter file renders in under one minute, leaving the trip to Paul's web site at: The fractal weather today was partly cloudy with a temperature of 83F 28C -- conditions the fractal cats found ideal. The dynamic duo showed their approval by sleeping side-by-side on the porch chair from 11am until 4pm. When the recent tragedy happened, my first emotional response was that of the Atheist I once was. I saw people asking how a good God could allow such a thing to happen. I saw them receive the only answer possible -- it's a mystery. I shook my head, knowing that to Atheists it was no mystery at all. I saw people trying to give a trace of comfort by telling each other that everyone would be reunited in heaven. I shook my head again, knowing that to Atheists the idea of heaven and an afterlife is no more than a comforting fantasy which humanity has evolved to enable men and women to cope with the existence of death. I realized the human tendency to believe the things that bring comfort and deny the things that bring despair. Then I thought of how it was religious fervor that had caused the death and destruction in the first place. I remembered how, all through history, similar deeds have been done by religious zealots in the name of their idea of God. This is one of the chief justifications for the existence of Atheism. Then I remembered that three people I know personally were missing, (though I have since contacted two of them). I was helpless. What could I say in the FOTD. My thoughts had returned to those of an Atheist. At times like these, Atheists wisely remain silent, retreating to the shadows, where their very rational beliefs based upon sensory input and scientific investigation can cause no one any additional grief. They hide there, pondering their realistic but despairing view of the human condition even while sincerely wishing it were not so. I was angry. But I could not publicly and unjustly attack all the members of one religion. At a time like that, I could not write the things an Atheist was thinking. So I had no choice but to end the FOTD. But I came back, because in the time I was away, I managed to find freedom from the paralyzing burden of Atheism -- a rational non-belief that has nothing to offer but despair. (Of course, it is not the job of Atheism to give comfort in times of grief.) How I found this freedom, as well as how I became a believer in at least one paranormal phenomenon, which I now feel does indeed exist even though it is rationally impossible, will be told in the upcoming FOTD's. But before starting, I really should find a way to connect my experiences to fractals. That's it for now. Until next time, take care, and the best is yet to come. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
MidgetWithDewdrops { ; time=0:00:50.80--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.023424823411983/0/1.230816e+008/1/180
params=1/-0.9/-1/-1.1/-549.998/800 float=y
symmetry=xaxis maxiter=282 inside=0 logmap=27
colors=00006C06C07D08E19F6AGBBHGCILDJQEGVGE_JBdK9i\
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ziazhZzhWzgTzgQzCWz22z85zD8zIBzNDzTGzYJzbMzZoz_lz`\
izafzbczcazdZzeWzfTzgQztnzZFz_Gz`HzaIzbJzcKzcKzdLz\
eMzfNzgOzMMzONzQNzRNzTNzUNzWNzXNzZOz`OzaOzcOzdOzfO\
zhPzgOzgOzAFzDGzGHzDCzCDz
}
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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times.
