Fractal of the Day
by Jim Muth

Galaxial Attraction ©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- July 13, 2010   (Rating 6)

Fractal visionaries and enthusiasts:

Due to the unusual colors of today's image, I wanted to rate it higher, but I just couldn't shake the feeling that I had seen something similar so many times before.   It takes more than just colors to make a great fractal image, so I finally settled for a rating of a 6, which is slightly above average.

The generating expression combines 1.5 negative portions of Z^(0.6) with 0.25 negative portion of Z^(6.4) and then adds (1/C).   The parent fractal is an area of scattered Mandelbrot sets with different degrees of distortion, all of them surrounded by clouds of smaller satellite M-sets, all the way to infinity.   Today's scene lies in a satellite of a satellite very deep in what appears to be an East Valley of one of the largest M-sets.

The name "Galaxial Attraction" means next to nothing.   It's probably a carry-over from my wonder years, when I wanted to be an astronomer.

Due to the extreme magnitude of the image, the mathtolerance entry in the parameter file is absolutely necessary.   Without it, all kinds of weird things happen.   The image actually lies beyond the range of perfect resolution, but the resulting breakdown is hardly noticeable.

The calculation time of 1-1/2 minutes is a fair price to pay for today's image.   The real bargain price may be found on the FOTD web site, where the already-calculated image may be viewed instantly.   The web site may be accessed at:
The temperature rose to 88F 31C in the early afternoon on Monday here at Fractal Central.   At 4pm however a thunder-storm moved in with a gust of wind and a brief downpour of rain.   By 5pm the temperature was a comfortable 73F 23C.   The storm dropped 1.5cm or just under 1/2 inch of rain, much to FL's satisfaction, but the rain here is still about 25cm or 10 inches below normal for the year.   The fractal cats braved the storm without dashing for cover.

The next FOTD will be posted in 24 hours.   Until then, take care, and every fractal should exceed the one before.

Jim Muth

START PARAMETER FILE=======================================

GalaxialAttraction  { ; time=0:01:33.41-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm maxiter=1800
  formulaname=MandAutoCritInZ function=recip float=y inside=255
  1/-55/0 logmap=394 periodicity=6 mathtolerance=0.05/1
  zrzzozzlzzhzzezzbzz_zzzzZ }

frm:MandAutoCritInZ   {; 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)+(p4)),
  k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
  |z| < l }

END PARAMETER FILE=========================================

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