Fractal visionaries and enthusiasts:

In today's image we return to the DivideBrot4 formula, one of the formulas I wrote while developing the FinDivBrot-2 formula, the one I now use most often for images with mixed characteristics.  The FinDivBrot-2 is satisfactory enough, but the DivideBrot4 does a few things better than the FinDivBrot-2.

Today's image shows one of these 'better' things.  The scene is located rather deep in the East Valley of the oversized parent fractal, which on the surface resembles an everyday Mandelbrot set.  Down at the depth of today's image however, things get out of control.  The quadratic minibrots have transformed into order-7 minibrots, but these minibrots have lost all pretense of 7-part symmetry, and are surrounded by patterns that appear to be a combination of Z^2 and Z^7 features.

The image shows an order-7 minibrot with every lobe doing something entirely different.  Some lobes connect out to the surface, while other lobes quickly come to a dead end.  Countless smaller minibrots fill the image, easily located by their brilliant orangish coloring.  Though these smaller minibrots share a similarity, no two of them are exactly the same.

The result of all this chaos is a rating of a 7-1/2, 1/2 point of which is due to the extra effort on the coloring.  (If I had totally eliminated the color bands, the image could have rated an 8.)  The calculation time of 3-1/4 minutes is not quite a bargain, but a fair price to pay.

The name "Two Times Seven" refers to the mixture of quadratic and order-7 elements in the image.

Another hot, hazy, muggy day prevailed here at Fractal Central on Thursday, with a temperature of 95F 35C.  Heavy storms threatened all afternoon, but at 6pm they had not moved in.  The fractal cats took things slowly, even asking for their treats in subdued slow motion.

The humans also had a slow day.  FL was concerned with a rain gutter that overflows on her garden, but the repair is not yet in sight.  The next FOTD will be posted in 24 hours.  Until then, take care, and when we finally do work out a theory of (almost) everything, will we be able to understand it?

Jim Muth
jimmuth@earthlink.net


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

Two_Times_Seven    { ; time=0:03:16.15-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=DivideBrot4 center-mag=+1.864192528962\
  /-0.0236455806899/1.28447e+009 params=7/7/2400/0
  float=y maxiter=6400 inside=0 logmap=696
  colors=00059L5AM5BN5CO5DP5EQ5FR5GT5HU5HW5GX5GZ5G_5\
  Ga5Gb5Gd5He9JdCLcFMbINaMO`PQ_SSZVVYZXXaZWd`YfcZhfc\
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  v``xc_yeXxaUxZRxWVwTZwQcwNhvKmvHrvEvuBzu8zu5Qd9WT8\
  aH8f68cABaEE_IGYMJWQLUUOSYQQaTOeVMiYKl_NmbQmeSnhVn\
  kXom_opapsdpvfpxaqrXqmSrhQocOlZLiUJfRHcPE`QCYRAVS8\
  SSCTR8_t4Ys6Xp8XmAXkCWhEWeGWcIW`JVYLVWNVTPVQRUOTUL\
  VUIWUG_XJc_LgbNkdQogSsjUrlZqnblphhrnctt_vzYtwWruUp\
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  uzlwzhyzeszcnzahz_czYZzWTzUOzSJzRIzQHzPHzOGzNGzMFz\
  LFzKEzJEzIDzHDzGFzFGzEHzD }

frm:DivideBrot4   { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1), d=real(p2)+100:
z=sqr(z)/(z^(-a)+b)+c
|z| < d }

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