Fractal visionaries and enthusiasts:

Today's image is obviously a Seahorse-Valley type Julia set.  So what then is it doing in one of the perturbed Mandelbrot sets, where it is surrounded by pieces of East Valley elephants?

Actually, it's no mystery at all.  The Julia shapes are universal in all orientations of the 4-D Julibrot.  The Mandelbrot shapes are special however, existing in their pure form only in the Mandelbrot planes, which are defined by real and imag 'C'.

Today's seahorse Julia shape is surrounded by elephants because the perturbed scene is located at the 'C' coordinates of Seahorse Valley of a minibrot that lies in East Valley of the Mandelbrot set.  The name "Seahorse Elephants" describes this relation.

I found the image by first zooming deep into the Seahorse Valley of the largest Minibrot in the radical complex of the period-14 elephant on the southern side of East Valley of the M-set.  Then, by using the evolver feature of Fractint, I found a perturbed value of Z where a chaotic area overlies the minibrot's Seahorse Valley.

The holes in this overlying layer appear as variations of the shape of the Julia set of whatever part of the Mandelbrot valley lies directly beneath them.  And the image holds some Julia-type figures that are even more interesting.  For more craziness, increase the maxiter and check the small but twisted set at the center of today's image.

The rating of a 7 is what I think the image is worth.  But I do not think the image is worth the 11-1/2 minutes it will take to finish the calculation.  To get a quick glimpse of the general shape, I suggest changing the outside from 'tdis' to 'iter' and setting the logmap to negative 215, which will shift the calculation to machine language and cut the calculation time to a few seconds.

I rendered the image with the outside set to 'tdis' because this spreads the colors in the best manner.  When the outside is set to 'iter' or any of the 'real' family, (real, iter, mult, summ), the color bands are either too narrow, giving a totally chaotic effect, or too broad, giving too many boringly flat areas.

The way to see the full craziness is to muster your patience and run the included parameter file, or to try the FOTD web site at:

       http://www.Nahee.com/FOTD/

Even with a mild temperature of 59F 15C, the heavy clouds and steady rain here at Fractal Central on Tuesday made things less than ideal for both man and cats.  The cats missed their sun, while the man wanted the work finished.  The cats got no sun, though, with some help from FL, the man did manage to get the work finished.  The FOTD fractal soon followed.

And speaking of fractals, the next one will be posted in 24 hours.  Until then, take care, and give homage where it is due.  I leave it to the individual to decide where homage is due.

Jim Muth
jamth@mindspring.com


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

Seahorse_Elephants { ; time=0:11:33.63-SF5 on P4-2000
  reset=2004 type=mandel center-mag=+0.2985719666032\
  641/-0.01848742793131565/7.471066e+009/1/142.5/0
  params=0.3101057985168/0.8009060914945 float=y
  maxiter=12000 inside=0 outside=tdis periodicity=6
  colors=000gzehzdizckzblzamz`nz`kzaizbgzcezdczeaxf_\
  vfYtgWrhUpiSnjQlkOjlMhlKfmIdnGboE`pCZqAXr8WrEXpJYo\
  OYmTZlYZkc_ih`hm`fraewadv`eu`ft`gs_hr_ir_jqZkpZloZ\
  m50B50C50D50E50F50H50I50I60K70K70K70N60P50Q40R31S2\
  2O11N02L02K53OA4RF6UJ7YO9`SBcVDhZElbHpeJtfMrfNqfPp\
  gPngRlgRjhThhUfhVdhWbiX`iYZiZWj_Uj`SjaQjaOkbMkbKkc\
  IlcGldEldCleAkfBjgBihBhjBglCgnCfpCerGdtKcvPcxUhzZm\
  zcmzemzgmzivzkzzmzzozzqzzszzuzzsrzrhzqZzpPyoMvnmsm\
  cplmnkcljmjichjUfkcdlcbmZ`mZemcmpUgtUbsUerSXrQXqOW\
  pMWpKVnIVmGUlEUkCUjATiATgATfBSeCSdCRcDRbER`EQ_FQZF\
  QYGPXHPWHOUIOTJOSJNRKNQKNPMeGLdHLcIKbJKbKJaLJ`MJ_N\
  I_OIZPHYQHXRGXSGWTGVUFUVFUWETXESYESZGT_IT`KUaLUbNU\
  cPVcQVdSWeUWfWWgXXgZXh`XiaYjcYkeZkgZlhZmj_nl_om_oY\
  XdJVUMUVOTVQTVSSVVSVXRWZRW`QWcPWePWgOXiOXlNXnNXpMX\
  rMXiNP`OHSP9JQ2KR3KR3KR4KR4KR5KS5KS6KS6KS7KS7KS7JS\
  7JS8JS8IS8IS8HS80S9Yv_Yu_ }

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