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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's fractal we return to the Z^(sqrt(2))+C figure for a look at another never-before-seen midget. With today's image, we have moved a bit farther out the log spiral. The result is that the parent fractal has been slightly rotated and has changed shape, though the overall characteristics remain unchanged. The midget at the center of today's image lies deep in a valley of its parent. The features surrounding the midget are unusually well defined for a scene in a fractal of such a low order, and are obviously related to the scepters that abound in the classic Mandelbrot set. I named the image "Reaching Out" for no particular reason, and rated it a 6. The parameter file renders in 22 minutes on a Pentium running at 200mhz. A faster way of viewing the image is to go to the Web at the URL's: The fractal weather today was pleasant enough, with partly sunny skies and a temperature of 48F (9C), which the fractal cats must have found enjoyable, for they spent almost 2 hours outdoors in the yard. And I spent almost as much time today pondering the mysteries of electrons, inventing experiments that would prove nothing. I dreamed up a situation that still has me puzzled. Imagine a closed container with a volume of 1cc. This container is filled with a perfect vacuum except for one lonely electron, which is placed inside when the container is sealed. One hour later, when the container is opened, two electrons are found inside. Obviously one of the two electrons, and perhaps both, has tunneled through the container wall from outside while the container was sealed. The question is, which electron is the one that was placed inside when the container was sealed. Since all electrons are exactly identical, does the question have any meaning? If the question is meaningless, does the concept of an individual electron have any meaning? Or are all electrons the same electron? While I'm trying to solve the mystery, I'll call it a night and close down the fractal shoppe. Until next time, take care, and take some more care. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Reaching_Out { ; time=0:21:54.96 -- SF5 on a p200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1
center-mag=-0.1698880815350267/+1.538364144638048/34\
96059/1/2.499 params=1.414213562373/0/0.5/0 float=y
maxiter=3000 inside=0 logmap=-493 periodicity=10
colors=000T7YT6XT6XS4VS3VR3TR2TR0SP0SP0RN0SP0RR2PS4P\
T7OVAOXCNYFLZHL_KKbNKcPJeSHfVHgZG<2>lfEmiEplCqnCsqBx\
tAzwAzy8zz8zz7zz6<2>zz8zz8xzAszA<2>ZzCSzCLzEFwEAqE<3\
>FXFGRFHLF<3>N0GO0GP0G<2>N0FN0FL0F<2>K6FK8FJ8FJAEJAE\
HBE<2>GCEGFEFHEFLEEOEESEEVCCZC<3>BgCAiCAlC8mC8pC8qCA\
jLAfTB_bBSjATi8Vg<3>3_b2aa0b_0cZ0bV0cX0cY0eZ<5>8gfAg\
gBiiCiiEjjFjlGjmHln<3>NmtOnuPnwPnwSpu<4>_qsaqsbqscsq\
esqfsqispjtpltpmtnntnqumsumtumuulwwlxwlzwj<2>zxizxiz\
zgzzi<3>zzjzzjzzjzzl<3>zzmzzmzzm<2>zznzznzzp<3>zzqzz\
qzzqzzq<3>xzlwzjwziuzgtzftzeszcqzbqzapz_pzZnzYmzXmzV\
lzTjzSjzRizPgzO<2>ezKezJczHgzBezFczHbzK_zNZzPYzSVzVT\
zYSz_PzbOzeNzgKzj<3>EzuCzxCzzBzzAzuAzn8zi7zb7zYgzC<2\
>czKbzNazO_zRZzTYzXXzZYzaXz_Xz_VzZVzZVzY
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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