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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: When I first saw today's picture, its texture reminded me of something. But I couldn't remember what. Then I suddenly realized that I was staring at a living coral reef. I promptly named the picture "Coral Reef" before the impression vanished. The formula behind the reef is once again my M-Mix4, the formula without apparent limits when it comes to creating new and interesting midgets. This time I subtracted a little Z^3 from Z^(-2) and delved deeply into the disorganized fractal that resulted. Unfortunately, the parameter file is slow, taking over 1/2 hour on a Pentium and fully half a day on an old-fashioned 486. Fortunately, I have foreseen the slowness and provided relief in the form of the JPEG file of the completed image, which has been posted to Usenet at: Now we get to what you've all been waiting for -- the fractal weather! It was an absolutely perfect early Autumn day here at Fractal Central, with the deep blue sky accenting the leaves, which are showing just the first signs of color. The temperature of 77F (25C) was perfect for anything including fractals. The next in the series of imponderable questions is, "Why am I myself instead of someone else?" The way I phrased the question it appears a bit ambiguous, so I will try to make the question clearer. Before I was conceived, billions and billions of people had been born, yet they were all someone else. What was so special about that single conception that made it totally different from every other conception that had ever occurred? Why was that particular infant my own conscious self instead of just another someone else who was not me? A corollary would be, "why is that 'one unique infant' a different infant for every person on earth?" As with the previous origin question, I do have definite thoughts on the topic, but getting those thoughts organized and into writing will take a day or two. So stay tuned, and enjoy the fractals in the meantime. Until another 24 hours passes, take care, and isn't life just one great big surprise after another? 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=======================================
Coral_Reef { ; time=0:39:50.91 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+0.46151020629591630/-0.2715498016590325\
0/1.439496e+009/1/57.5 params=-0.3/3/1/-2/-0.4/0
float=y maxiter=9000 bailout=25 inside=0 logmap=634
symmetry=none periodicity=10
colors=000MZr<4>HUmGTlFSk<15>VDSWCRXBQ<2>_8M`8L_7N<\
19>S5gS5hR5i<2>Q5lQ5mO7p<3>IByOLnTUc<3>KYkIZmF_o<3>\
7cw<18>BepBeoCeo<2>CenCenBdl<17>2YL2YJ1XI<3>0WC<9>L\
`8N`7Pa7<2>Vb6Xb6Yd9<2>_iI_jLafM<3>gTQhPQjMR<3>o8U<\
18>GLRELRCMR<3>5OR<7>NGiPFlREn<2>XBuZBwZBw<6>cBxcBy\
dBydByeBy<3>iEzjFzkGzlHzmIzmJz<38>mKz
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Coral_Reef { ; time=0:39:50.91 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+0.46151020629591630/-0.2715498016590325\
0/1.439496e+009/1/57.5 params=-0.3/3/1/-2/-0.4/0
float=y maxiter=9000 bailout=25 inside=0 logmap=634
symmetry=none periodicity=10
colors=000MZr<4>HUmGTlFSk<15>VDSWCRXBQ<2>_8M`8L_7N<\
19>S5gS5hR5i<2>Q5lQ5mO7p<3>IByOLnTUc<3>KYkIZmF_o<3>\
7cw<18>BepBeoCeo<2>CenCenBdl<17>2YL2YJ1XI<3>0WC<9>L\
`8N`7Pa7<2>Vb6Xb6Yd9<2>_iI_jLafM<3>gTQhPQjMR<3>o8U<\
18>GLRELRCMR<3>5OR<7>NGiPFlREn<2>XBuZBwZBw<6>cBxcBy\
dBydByeBy<3>iEzjFzkGzlHzmIzmJz<38>mKz
}
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.
