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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's average fractal reminds me of some kind of berries. Maybe raspberries, maybe strawberries, I'm not sure. Due to my uncertainty, I named the picture "Something-Berries". The parent fractal was created by another of my deceptively simple formulae. This time, 4Z^(-1.45)-2Z^(-14.5)+(1/C) did the job. This formula, when iterated, draws a Mandeloid with several large bays. Today's scene is located on the edge of one of the large bays, near the tip of the star of a tiny radical (or bud complex). The resulting picture is not great, but it's not bad either. It's just about average, which justifies the rating of a perfectly average 5. The parameter file produces a finished image in almost exactly 10 minutes on my tired, worn-out old Pentium 200mhz machine. But the image can be downloaded in 1/10 of that time from: The fractal weather today was sunny and very average, a condition which the fractal cats found very enjoyable. Average for this location at this time of year is a high temperature of 82F 28C. My ponderings today focused upon the small but existing human ability to see random glimpses of the future. I wondered whether this ability is a vestige of a much wider ability to see the future that existed in earlier stages of human development, or whether it is the first sign of an ability that is just starting to evolve in man. Since knowing the future would be a great advantage, those with this ability would have a greater likelihood to survive and produce offspring to which they would pass on the ability. If our distant ancestors had possessed any significant degree of precognition, the percentage of humanity with this ability would have increased over time, until by this point in human evolution, every one of us should have it. But the present human ability to see the future is not close to being universal. It is rare enough in fact that some still doubt its existence. This leads me to conclude that precognition is not a vestige of an ability we have lost, but rather the spark of an ability, which because of its survival advantage, will become more widespread and ultimately universal in our distant descendants. Even more interesting, when seen from a four-dimensional spacetime viewpoint, knowing the future can be taken as the same event as changing the past, but viewed from the opposite direction. Does our present slight ability to see the future imply a similar slight ability to change the supposedly fixed past? I wonder. That's it for today. Until next time, take care, and for every mystery that is solved, two more will appear. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Something-Berries { ; time=0:10:01.54--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+1.50065188510701600/+0.357694228187471\
10/323066.5/1/57.499 params=4/-1.45/2/-14.5/0/800
float=y maxiter=2400 inside=0 logmap=109
colors=0005bt6dt6fu8gv9hv9ixBkxBlyCmyDozDpzErzEszG\
tzGvzIrzLozMlzPizRgzTdzWazXZz_XzaUzcSzfPzgNzjKzmHz\
nFzqCzrCztDztGzuKzuNzuPzvTzvVzvYyxayxdxxgvykvymuyp\
tzttzwrzzvzzruynnwkhvgatcXt`RsXLrTGpQ9oM4mI0t90mG8\
hLHaQQXW_S`aTYcUWdVVfXRgYPhZNkZLm`InaHobEqdCrfBtg8\
vg5xh4yi1zk0zl0zm0zm0xo0qp0jr1dr4Ys6Rt9LvCGvE9wH3y\
J0zI0yL0tN0pQ0lR1hV3dX3`Y4X`5Tc3On5Pd8QXBSNDTGGU6I\
V0JX0JU0JS5JPCJNIJKPJHWJFaJCh0h90h81h83h64i65i56i4\
8k49k3Bk1Ck1Dl0El0Gl0Hm0Im0Jm0Pi0Lm0Ip3Gt9DwEBzL8z\
R5zX3zc0zj0zt0zo0zk0zh0zd0za0vY0rW0mR0iP0fL0aI0YE0\
UC0Q80N50I10G00I04L18N3CP4GQ4JT5NU6RX8WY8_`9caBgdC\
hh9kfCmbEn`HoYIqVLtTNuQQvORxLVyIXzG_zH`zIczKdzLfzN\
gzOhzPjzQkzQmzSnzSozTqzTrzUtzUuzVvzVxzXyzXzzYzzYzz\
ZzzZzz`zz`zzazzazzbzzbzzbzzdzzdzzdzzfzzfzzfzzgzzgz\
zgzzhzzhzzhzzizzizzizzlzzlzzmzzmzzozzozzpzzpzzpzzp\
zzpzzpzzpzzpzzpzzpzzpzzpz
}
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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