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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In today's image things start to go wrong. The midget at the center is clearly of the quadratic variety, as are almost all midgets in fractals created by the MandelbrotMix* series of formulae. But the expected 2-4-8-16... series of elements leading toward the midget is not as well defined as it might be. The confusion is just starting to appear, but it is there, and from here on, the confusion will only increase. The parent fractal of today's image is virtually the same as the parent of yesterday's image -- a seemingly harmless mixture of Z^3 and Z^4 that would be expected to do little but create a routine combination fractal. In the world of fractals however, surprises are common, which is why I find fractals so fascinating. The surprises coming in the next few days are some of the greatest I have yet stumbled upon. I have named today's image "X-Y Mandel Fractal". Something about the image reminds me of pictures I have seen of the X and Y chromosomes that determine an individual's sex. I believe all individuals start as women, but half are mutated into men by an X-Y chromosome. If this is true, then half the population of earth consists of alien mutants bent on death and destruction. After watching the news, I guess it's true! Before getting sidetracked into politics, an ever-present danger, I must get back on the fractal track and admit that I could rate today's image no higher than an average 5. When the render time of 4 minutes is taken into consideration, the overall value jumps to 118. The best value of all is to download the GIF image file from the FOTD web site at: A warmer temperature of 48F 9C, lots of sun, and lighter winds gave the fractal cats a pleasant afternoon in the yard here at Fractal Central on Tuesday. Today is starting still warmer, but with clouds moving in, the duo might not be as happy. For me, it looks like another routine day of getting the work finished, then exploring in Fractal Land. So until next time, take care, and good fractals make unhappy cows give more milk. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
X-Y_Mandel_Fractal { ; time=0:04:13.92--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.52128983921205970/+0.000169467990356\
02/988403.5/1/90/3.88578058618804789e-016
params=1/3/0.3555/4/0/0 float=y maxiter=1200
inside=0 logmap=78 periodicity=10
colors=000AGQAHR9IS9JT8KU8LV8LW7MX7MY6NZgzzTzxRzvV\
vsZrpbntfjwifzdZu_RqVJmz_KzUKzBKxI2uHCsGLpFVnEclI_\
jMWhQTfTPdzMbuIapFdkKffPicUk`YnYbpVgrSkqPhqSfqWcp_\
arcZvgXzkVg1ElHBqW9zj7zhBzfEzdHwbKt`OqZRnXUkWXhTZe\
Q`bNa_KcXHdUEfRBgOKjLSlI_noVopRpqNqrIrsEstAtu6trBn\
pFhnKblOXjTRhXMoi`lgWjeShdOfbKdaGbcCad9`e6_f3Zg0px\
_lx`hwadwb_wcWvdSveOvfhVdjSkkQqjR_jRJZOLNLMMQOMVQL\
_RLdTLiVKnWKsYKxZaHHWJKRKNMLQGNTBOW6PZCSbIUfNWjTYn\
Z_rcaveXtfSshOriJpkEolAneBmZBlSCkLCjEDi8DiGEhNFgVF\
faGeiHdpHcfQWYZOOgGFo8JkFNgMQdSU`ZYXe`UkZKlXAlW0lS\
1mP2nM3oI4pF5qC5r9Jn6Xj4igHccUY`fSYsMVtQZtTatXdt_g\
i_j_`mQapGbsFcrEdqDepCfpBgoAhnAinOjZ`kJml4jm9hnEfo\
IcpNaqS_rWWsQTtKPuDMv7Jw1DxB8yK3zT9zXFz`LzdRzhXzlb\
zphztmzwjzrgzndzjaze_zaXzYUzTRzPPzLLzQIzVEzZBzc8zg\
9zh9zhAziAziAzjBzjBzkCzkCzlCzlDzmDzmEznEznEznDzlDz\
jDzhCzfCzdCzbBz`BzZBzXAzV }
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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