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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: I named today's fractal "Gossamer" when I noticed the vague resemblance between the main feature and the sneaker-wearing monster of that name, with orange hair, which appears in several cartoons, and is usually tamed by Bugs Bunny. The fractal is another of those unfamiliar slices of the very familiar collection of Z^2+C Julia sets. In this case, the scene is in a perturbed part of the Seahorse Valley area. The orientation of the slice is 42 degrees from the Julia direction toward the Rectangular direction. The parameter file is quite a fast one. The effort of copying the file to the Fractint directory with the .par extension etc. will take longer than running the file. About the same amount of effort will be required to download the completed image file from Usenet at: Enjoy today's speedy image, because tomorrow's curious image will be the slowest in the history of the FOTD. The fractal weather was perfect today, the temperature of 81F (27C) and sunny skies being absolutely perfect for anything imaginable. The fine day was a bit too lazy for intense philosophical pondering, but I devoted some effort to the current question, which is "Why am I myself and not someone else?" The rational answer to this question is, "I am myself because of an extremely lucky accident of nature." And of course, the world is then assumed to be populated with 6-billion other equally-unlikely accidents. However, this answer is not an answer at all; in fact, it is hardly more than a restatement of the question. The lucky accident referred to in the rational answer is the particular group of individual atoms and sub-atomic particles that composed the ovum and spermatozoon from which I was conceived. It is assumed that if one electron had been different, someone else would have resulted from the conception. There are many questionable aspects to such an assumption. I will name four. To begin, quantum mechanics shows that it is meaningless to speak of particular or individual electrons or atoms. All atomic particles of the same type are indistinguishable; basically, all particles with the same description are the same particle. Second, identical twins come from the same fertilized egg, yet they are totally separate self-awarenesses. Third, as living beings, our bodies are composed of atoms that are constantly changing, yet we remain the same person. At what stage of fetal development are the atoms of our bodies supposed to cease determining our conscious identities? Finally, there is the virtual impossibility of each individual ever having happened. What is the number of different awarenesses that are possible? If it is not infinite, it is beyond any imaginable number. The chances of any one of us ever coming into existence is one divided by this infinity -- a number just about equal to zero. Apparently, it is impossible for any one of us to exist, yet here we are. How can this paradox possibly be explained? It's quite a challenge I've set for myself, but I'll tackle the paradox in the near future, possibly in the next FOTD. Until tomorrow, which never comes, take care, and I'll see you. Jim Muth jamth@mindspring.com |
START FORMULA==============================================
multirot-XY-ZW {; draws 6 planes and many rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(z)+c,
|z| <= 36 }
END FORMULA================================================
START PARAMETER FILE=======================================
Gossamer { ; time=0:00:44.66 0n a p233, SF5
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=1
center-mag=0.131019/-0.00183134/2.6175/1/-67.5
params=48/90/-0.5/0/-0.76/0 float=y maxiter=2400
bailout=25 inside=0 logmap=5 symmetry=none
periodicity=10
colors=000SAYSAY<12>BPeAQf9Sg<3>3Wj<11>BRZCQYDQX<2>\
FOUGNTFOU<17>C`iCajCbk<3>Cdn<21>YfPZfN_fM<3>cfI<2>N\
kgHloAnw<6>JhwKgwLfw<2>PcwQbwQdx<10>`JuaHubFt<2>e9t\
f7te8s<16>_BnZBnZCn<2>YCmYCmZEk<20>seHtgFuhE<3>ym8\
<19>XREVQEUPE<3>OLFPJD<14>7We5Xg4Yi<2>1`o0`p1ao<10>\
2hn3im3im<3>3lm0rq<4>BQ`X5VW6WV7W
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Gossamer { ; time=0:00:44.66 0n a p233, SF5
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=1
center-mag=0.131019/-0.00183134/2.6175/1/-67.5
params=48/90/-0.5/0/-0.76/0 float=y maxiter=2400
bailout=25 inside=0 logmap=5 symmetry=none
periodicity=10
colors=000SAYSAY<12>BPeAQf9Sg<3>3Wj<11>BRZCQYDQX<2>\
FOUGNTFOU<17>C`iCajCbk<3>Cdn<21>YfPZfN_fM<3>cfI<2>N\
kgHloAnw<6>JhwKgwLfw<2>PcwQbwQdx<10>`JuaHubFt<2>e9t\
f7te8s<16>_BnZBnZCn<2>YCmYCmZEk<20>seHtgFuhE<3>ym8\
<19>XREVQEUPE<3>OLFPJD<14>7We5Xg4Yi<2>1`o0`p1ao<10>\
2hn3im3im<3>3lm0rq<4>BQ`X5VW6WV7W
}
frm:multirot-XY-ZW {; draws 6 planes and many rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(z)+c,
|z| <= 36 }
END 19.6 PAR-FORMULA FILE==================================
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