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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The equal-iteration bands that appear in nearly every FOTD image are sometimes seen as an undesirable result of the 256-color GIF palette. At other times, the bands make the picture. Today's image is one of the best examples of a picture made by its bands. I named the image "Iteration Bands" as a simple description. Then I rated it at a 6. The iterated formula takes the tiny difference between Z^(-1.49) and Z^(-1.51), and multiplies it by a factor of 200, resulting in a parent fractal that extends beyond the default screen, but is worth an outzoom to bring it into view. The image renders from the parameter file in a little under 7 minutes on my tired machine. It downloads in less than half the time from: The fractal weather today (Sunday) here at F.C. featured heavy clouds with rain and thunder. The cats accepted the temperature of 81F 27C with barely a shrug, but disapproved strongly of the rain and thunder, letting me know it by making themselves quite obvious around Fractal Central. As I often state in my philosophy, I feel that a great mystery lies behind the surface appearance of the world. That mystery is not the question of the existence of God, or the likelihood of an afterlife. Nor is it the meaning of life, which may have no meaning within our understanding of the word. In my opinion, the greatest mystery is how I came to be myself and not merely one more someone else who is not me. If I could find the answer to this single question, I suspect that the answers to the other questions would follow automatically. I am unique. I am the only self-awareness of which I am directly aware. Wherever I may be, the universe is always centered around me. There is no other apparent center. These are not statements of an overblown ego. To me, they are self-evident facts which I experience every moment of my life. These facts by themselves would appear to make me the most important being in the universe. But unfortunately for me, there are over 6-billion people on earth who can truthfully claim the same honor. I'll discuss some of my ideas about this type of stuff in the FOTD discussions to come. Right now... Something (like the clock on the wall) now tells me that it's time to tackle the things that need to be done. So while I'm occupied with other things, take care, and see you in 24 hours. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Iteration_Bands { ; time=0:06:33.60--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-1.42277533169381500/+3.340461066977218\
00/9.005038e+010 params=200/-1.49/-200/-1.51/0/525
float=y maxiter=1200 inside=0 logmap=138
colors=000b83a80fA3kB6pD9uECzFFxNJwYNvcQthUssYrv`i\
gQaUGWPAQKAK0AF0AJHANNARTAVZPZcUXfYViZUl_So`RraPub\
OtcNtSNqGNo5Tk4Zg3cc3i_2oW1tS1sQ5sO9sMDsKHrILrGPrE\
TrCXk9cd7iY4pR2vPApOIkNPeMX`LdVKkQNkOPkNRkLUkPZkUc\
kZhkcmkhrkmwirzgwzhtzhqzhnzhkzihwieribmi_hiXdjUbjR\
`jOZjLYjJViKThLQgLOfMLeNJdNGcOEbPBaP9`Q6_R4ZR6XT7V\
U9UVASWBQXDPYENZGL_HK`IIaKGbLFcNDdOBePAfND`LGVKJQI\
MKHOFIQHIRIJSJJUKKVLKWMLXNLZPM_QM`RNaSNcTOdUOeVOfW\
Wcac`gkYmhWjeUgbSd_QaXOZUMWRKSOJTOJUOJVOJWOJYOK_OK\
aOKcOKeOKgPLiPLkPLmPLoPLqPLsPMuPMwPMyPMzPMzPMzPNzP\
NzPNzPNzPNzPOzPOzPOzPOzPOzPPzPPzPQzPRzPSzPTzPUzPVz\
PWzPXzPYzPZzP_zP`zPazPbzQczQczQczQczQczQczQczQczQc\
zQczQczQczQczQczQczQczQczQczQczQczQczRczSczTczUczV\
czWczXczYczZcz_cz`czaczbczcczcczcczcczcczcczcczccz\
cczcczcczcczcczcczcczcczcczcczcczcczcczcczcczcczcc\
zcczcczcczcczcczcczcczccz
}
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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times.
