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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Yes, I realize that it's Saturday evening as I write this, and Saturday evening is the time for the junky old sci-fi movies to appear on the TV. Of all the good oldies, "Invasion of the Body Snatchers", from the 1950's, is one of the best. In that movie, vegetable pods from outer space land in a small California town and begin taking over the personalities of the inhabitants. The enclosed shapes surrounding the tiny midget in today's picture remind me of those pods from space. The name "The Fractal Pods" seemed perfectly appropriate, so that's the name I gave the picture. When it came time to decide on a rating, I found myself undecided between a 6 or a 7. I decided on a rating of 7, as I feel I have been a bit too conservative in my ratings. After all, what good is having a rating of 9 or 10 if nothing ever rates that high? I colored the image so as to emphasize the outlines of the pod-like shapes surrounding the little lost midget at the center. When today's image was complete, I zoomed into it, to the point where eight pods surround a much larger midget. But even though I applied the same color palette to this deeper zoom, the image was not as striking as the one with four pods, which made the lofty status of FOTD. The scene of today's image is another one buried deep in the second version of the 'parent' fractal. Instead of being located in the 'fan', today's scene is located off-center of a ring to the lower-left of the fan. The four pod-like structures are not quite like anything I have seen in fractal-land. The MandelbrotMix4 formula certainly is surprising. The parameter file renders in a slow 10 minutes, which makes the couple minutes it will take to pick up the GIF file from: Before getting on to the all-unimportant weather, I must announce that one more wasp has hatched from the mud-nest sitting high under the roof of the fractal porch. Now as for that weather . . . The fractal weather today was once again near perfect, with lots of sunshine and a temperature of 85F (29.5C) to keep the cats contented. This morning on the philofractal list I found a letter from Morgan Owens, containing one very terse comment, which despite its terseness, gave me a lot to think about. Morgan wrote: > What I find futile is how, no matter how many times I state my > position, my debating opponents constantly misrepresent it. So > why should I bother? And I now reply: This mis-representation of ideas always happens in debates of the kind we've been engaged in. It seems to be inevitable. Actually, we have nothing tangible to debate other than the mis-interpretation and mis-understanding of our ideas. We all receive basically the same sensory input as source material. If we didn't mis-interpret one another, we would all agree, and there would be no debate. That would be very boring indeed. As an example of interpretation, take the question of whether I believe in God. Since each individual asking the question holds their own idea of God, the answer I would give would depend on the idea of God held by the one who asked the question. If I were asked whether I believe in an invisible super-magician out beyond space, I would reply, "no." If someone who defined God as the natural laws of the universe were to ask whether I believed in their idea of God, I would reply, "the laws certainly exist, but in order to be considered God, the laws must be conscious." If someone were to ask whether I believed that the universe, including all its discovered and undiscovered parts, is conscious, I would reply, "yes, and this universal consciousness is as close as I can come to communicating my idea of God." Maybe we should each write a paragraph or two, clearly stating our world views. This would help avoid mis-representation. My paragraph might go as follows: I consider the objective and subjective worlds to be two different aspects of the same underlying unity, in much the same manner as M-sets and J-sets are different aspects of the same Julibrot. I feel that true knowledge may be gained through subjective experience as well as through objective experience, though I consider only knowledge gained through objective experience to be scientifically valid at the present time. I understand and enjoy the discipline of science, but feel concern about the way science ignores metaphysical things, thus creating a self-imposed blindness that has cast our culture adrift into a spiritual vacuum. And that abrupt conclusion will have to end the day's philosophy. It's getting late and the fractal cats want to eat. Until next time, which will arrive in 24 hours, take care, and be at peace with your fractals and yourself. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Fractal_Pods { ; time=0:09:52.37 -- SF5 on a P200
; Version 2000 Patchlevel 14
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-4.227215139919892/+3.564638496815993/553\
27.29/1/172.5 params=-1/-11/-11/-1.08/0/800 float=y
maxiter=1800 inside=0 logmap=179 periodicity=10
colors=00011I<3>11K21L31N41N<2>51R51S71S<2>81X80Y80Y\
80ZA0`A0aA0b80aA0bA0bA0bA0d<2>B0eB1eB1eC2fC3fC3fC4hC\
5hD5hD7iD8iD8iDAkFBkFBkFClFDlGCmFDlFFlFFkFGkFGkFHiFH\
iDIiDIhDKhDKhDLfDMfDMeCOe<2>CPdCQdCQbCSbAQdCSbDUaFU`\
GV`HVZIWYKYYLYXMZVOZVP_TQaSSaRUbRVbPWcOYeOZeN_fLYbPa\
fLejJhoGipIipIjpIjpJjrJlrJ<2>msKmsKosKosLpuLpuLpuNru\
N<2>svOsvOuwOuwOvwPvwPvyPwyRwyRyyR<5>zzTzzTzzTzzVzzV\
zzVzzVzzX<3>zzYzzYzzYzzYzvVzpTziRwcPuaOrZLoYKlWJiUGf\
PFcLEaGBZCAY88Z8AZAA_AA_BB_CBaFBaGBaGDbHDbHDbIDcKEcK\
EeLEeLFeMFfOFfOFfPGhQGhUGhVGiYI<2>jcJjeJlhJljJljKmlK\
mlKmmKooLooLppLppNprNrsNrsNruOsuOsvOsvOuuPuuPvuRvsR<\
2>wrTwrTyrTypVzpVzpX<2>zoYzoYzmZzmZzlZzl`zj`<3>yhayh\
ayfayfbyebyebzca<3>zcXzcVzcT<19>zcT
}
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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