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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: Weather report -- mostly cloudy with a temperature of 72F (22C) and a light rain in the evening -- the perfect recipie for a fractal. To prepare today's fractal I once again cranked up the MandelbrotMix4 formula and let it loose. I added 11 parts of Z^(-11) to Z and watched to see what would happen. What happened was the generation of a fractal with a mandel-shaped hole at the east edge of a Z^(-11) figure. Examining one of the side lobes of this Z^(-11) figure where I had expected to find nothing, I found today's image. I named the picture "Patches" when I noticed how the colors are spotted through the image like the patches on a clown's costume. An earlier color palette inspired the name "Shark's Teeth", but that name just didn't sound as pleasant as "Patches", so I abandoned it. The parameter file is fast: the picture file is even faster. The picture file has been posted to: With the fractal cats behaving themselves, (mainly because I didn't let them outside), there were far fewer irritations today, which gave my philosophical energies a chance to accumulate. I applied those energies to the problem of why I am myself and not someone else. (It will take two days to get my ideas across.) It is a difficult problem, ambiguous and hard to state. Some will deny that a problem exists at all. Some will say, "I am myself because I am myself -- it could not be any other way". This reply simply tosses the awkward problem into the corner, where it may be comfortably ignored in favor of more practical intellectual pursuits. Never content to accept things the way they are, I choose not to ignore such difficult and perhaps foolish questions. Instead, I spend my meager idle time pondering the imponderable. I begin with the rational explanation. Rationally speaking, during a person's lifetime, the chance of that person's present existence is 100 percent, the chance of his pre-birth existence is zero percent, and the chance of his after-death existence (ignoring the hypothetical immortal soul) is virtually zero. Before the person was born, it was meaningless to ask the chance of his past, present or future existence, for the person had not yet been defined. After the person's death, the chance of his past existence will remain 100 percent; the chance of his present existence will be virtually zero percent, for he will be dead. The chance of his reappearance in the future (ignoring reincarnation) will be infinitesimal, but not quite zero, because his appearance from nothing, having already been demonstrated to be possible, could just possibly happen again. The details of this scenario could be debated, but this is basically the common-sense appraisal of the likelihood of an individual's existence. The conventional religious outlook is also based upon a common sense approach, though in this case a different reality is assumed. Unfortunately, the religious approach does nothing to clarify the situation. According to conventional religion, a person is actually an immaterial immortal soul. When the person was conceived, God created a soul and inserted it into the person's embryonic body. Of course, after the person's body dies, this soul, which is actually the person, will depart the body and, carrying the awareness with it, continue to live in the next world. It can immediately be seen that this belief merely pushes the problem back one step. In addition to the fact that no evidence of souls has been found, the unanswerable question remains. It can still be asked, "why is this particular soul myself and not just another soul that is not me?" When considered carefully, the question seems impossible to answer, almost absurd. But when a question seems impossible to answer, there is often something wrong with the assumptions behind the question. Could it after all be that the question itself is based upon a wrong assumption? It possibly could be. Tomorrow, I'll explore this aspect. Until then, take care, and things are never so good that they can't get better. Jim Muth jamth@mindspring.com |
START FORMULA==============================================
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 FORMULA================================================
START PARAMETER FILE=======================================
Patches { ; time=0:00:52.39 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.7222600050579036/+0.6770075491941554/\
700.6188/1/-172.499 params=11/-11/1/1/0/0 float=y
maxiter=2000 bailout=25 inside=0
logmap=7 symmetry=none periodicity=10
colors=000KHBqY9pc7pi5<2>zkY<7>T60KG4CU84iCK_AUR9\
<5>w60mA2cD4XG6<3>KTEHN9EH5gc`<4>pup<3>BIKBINl`U<4>\
aWDKUAUR9OU8<2>8U76RH5ZQBcS<4>dZ__cLVg7<2>bxJWyBQz3\
<7>gzM<2>`zs<3>mzXpzSvzi<5>Ez3<7>YzmXziWzf<7>xzD<6>\
xz8<2>Qzx<7>xz4czTKzqTza<6>szk<7>`zzhzr<5>WzW<2>jz6\
TzIBzT<4>5zh<3>VzF<5>Czs<2>Iz`<7>0zYkzvIzJYzj<4>Uz`\
qzc<4>Yz_uzQ<4>YzZfzB<11>VzZazZ<6>Vz_Bzabz5<11>UzYT\
z3<9>UzRrzD
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Patches { ; time=0:00:52.39 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.7222600050579036/+0.6770075491941554/\
700.6188/1/-172.499 params=11/-11/1/1/0/0 float=y
maxiter=2000 bailout=25 inside=0
logmap=7 symmetry=none periodicity=10
colors=000KHBqY9pc7pi5<2>zkY<7>T60KG4CU84iCK_AUR9\
<5>w60mA2cD4XG6<3>KTEHN9EH5gc`<4>pup<3>BIKBINl`U<4>\
aWDKUAUR9OU8<2>8U76RH5ZQBcS<4>dZ__cLVg7<2>bxJWyBQz3\
<7>gzM<2>`zs<3>mzXpzSvzi<5>Ez3<7>YzmXziWzf<7>xzD<6>\
xz8<2>Qzx<7>xz4czTKzqTza<6>szk<7>`zzhzr<5>WzW<2>jz6\
TzIBzT<4>5zh<3>VzF<5>Czs<2>Iz`<7>0zYkzvIzJYzj<4>Uz`\
qzc<4>Yz_uzQ<4>YzZfzB<11>VzZazZ<6>Vz_Bzabz5<11>UzYT\
z3<9>UzRrzD
}
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 19.6 PAR-FORMULA FILE==================================
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times.
