|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Converging strings of pearls. Radiating strings of diamonds. Diamonds without end. An infinity of fractal diamonds -- all this in a simple fractal. That fractal is today's fractal, and once again, the fractal comes from the unlimited reservoir of the MandelbrotMix4 formula. The parent fractal is an asymmetrical Mandeloid rotated 110 degrees CCW from the normal left-is-west position. The midget in today's image lies at the tip of the period-2 tail of the parent fractal. The expression that drew the image is Z^(-0.6)-1.2Z+1/C, a mixture of positive and negative powers of Z. Such a mixture often draws fractals with eye-shaped features, or in the case of today's image, perfectly symmetrical sharp-angled eye-shaped features that resemble diamonds. At first glance the picture appears to have X-axis symmetry. This is an illusion. Though it cannot be noticed in the image, the scene is in no way symmetrical. I named the picture "Infinite Diamonds" because the number of diamonds in it is infinite. Of course, infinity is not a number, it is the condition of being without limit, which is just another way of saying that the number of diamonds in the picture is without limit. The picture rates a perfectly average 5 on my 0-to-10 scale of fractal value. If I had more time, I could have worked out a more suitable color scheme, and with more time, I also could have found a midget with more diamonds. As an extra bonus, the parameter file is the fastest in several days. On a tired old P200 machine, it runs in 36 seconds. The time spent copying the file to the Fractint directory will be longer than this. For those who wish to avoid the hassle of copying and naming a file, the GIF image has been posted to the Usenet binary group: The weather today here at Fractal Central was sultry. The day started with a thunder-shower at daybreak, and ended with another thunder-shower just before sunset. Neither of the showers amounted to much. The temperature of 91F (33C) was a bit too warm for the fractal cats, who preferred to pass the day lounging in the air-cooled fractal room. The fractal philosophy stirred only a tiny bit as I pondered the mysteries of the fourth dimension with its metaphysical four-dimensional objects composed of curved and flat three-dimensional spaces. The surfaces of these 4-D objects are 3-D boundaries with 3-D volume. The task of visualizing an object with a 3-D boundary-surface is impossible, yet there appears to be no reason why this must be so. The math flows smoothly from one dimension to the next, with nothing special about 3-space. Perhaps it's all in our minds. I'll ponder this aspect in far more depth when the muse stirs. Regardless of where the secret to the fourth dimension lies, it's now time to shut down the fractal shoppe for another evening, shoo the cats, and call it a day. Until tomorrow, when I'll return with more goodies, take care, and when good fractals happen to good people, everyone is happiest. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Infinite_Diamonds { ; time=0:00:36.26 -- SF5 on a p200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip
center-mag=-0.03474520578034267/+0.08388234702240095\
/9.91477e+010/1/-112.5 params=1/-0.6/-1.2/1/0/0
float=y maxiter=1200 bailout=25 inside=0
logmap=16 symmetry=none periodicity=10
colors=000668064<3>6DG7FJ9HM<2>DMVENmGPmrRzrSzGcYFc_\
<3>BcN9bK8aH<2>5Z74Y45X8<2>7UK8aO<3>BdcCegCekDfoEgsE\
gv<7>PiqQipRip<3>Win<4>SjZRkWQkTQkQ<3>NnEMoBLp8Lq5Rr\
AWs4<3>qw4vx4wyOxzg<6>kznizogzp<3>`zt<3>eztfztgzt<9>\
izkjzjjzi<3>jzf<2>Zzo<3>bzpczqdzqezqfzqfzq<8>izeizci\
zb<3>jzY<3>XzMTzKQzH<3>Cz6<6>6zT5zW5zZ<3>2zj<4>jzWsz\
Urzv<7>vzovznwzn<2>xzkxzkwzh<3>wzYvzVvzT<2>vzLhzl_z`\
SzP<7>ZzF_zE`zC<3>cz8NzV7zp<3>3zj<3>LzbQz`UzZZzXbzW<\
6>`zd`ze`zg<2>`zj`zkZzf<3>TzQSzMRzI<5>JzhQzKJzGDzC
}
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==================================
|
times.
