Fractal visionaries and enthusiasts:  

As far as I know, the four-dimensional HyperMandelbrot set is virtually unexplored, so with today's image I have decided that it's time to do some exploration.

To begin the investigation we see what trouble we can get into in the Seahorse Valley area of the hyper-M-set.  As the coordinates show, today's scene is located deep in the north branch of the valley.  I named the image "Hyperseahorses" because of its location in its parent fractal.  The diagonal shaft is the actual north branch of the valley, which is oriented so that north points to the lower right.

The main shaft of the quadratic valley is apparent enough, but all the other stuff is part of the hyper-M-set.

I see almost nothing in the image that even vaguely resembles a seahorse.  What I do see is a medley of features that have little resemblance to the features of the classic M-set.  It will take quite a bit of experimenting to make sense of the things in this image and images to come, but being curious, I'll certainly give it a try.

The art rates a 6.  I see nothing very artistic in the image.  The math however rates a 9, since I'm sure to find a lot of interesting quirks in this area.

The image calculates in 3 minutes on the average SOTA machine that does not crash when it senses the presence of a DOS program.  The web sites can bail out these machines that panic when DOS appears.

Except for a period of light snow in the afternoon, today was partly cloudy and chilly, but pleasant enough, with a high temperature of 21F -6C.  The fractal cats had a lazy day -- typical for a ten-year-old cat but unusual for a five-month-old kitten.  I had a lazy day to myself, while FL spent the week-end visiting with old friends back in Baltimore.

The next FOTD will probably be posted in one day.  If it is not, then it will appear in two days.  Until it does appear, take care, and who is really running the world.  Is it the world's governments, the big corporate conglomerations, or could it be the aliens from Sirius C?

Jim Muth
jimmuth@earthlink.net


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

Hyperseahorses     { ; time=0:03:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=t float=y
  center-mag=-0.7500079994/+0.0019964869/37374/1/\
  -122.5/0 params=0/0/0/0/0.25/0/1e-100/0
  maxiter=2250 inside=0 logmap=1540 periodicity=0
  colors=000WFSXFSYFRZFR_FR`FRaFRbFQcFQdFQeFQfFQhFPi\
  FPjFPkFPlFOmFOnFOoFOpFOqFNrFNsFNtFNvELuFNuGPuHRuIS\
  uJUuKWuLXuMZuN`uOauPcuQeuRguShuTjuUluVmuWovWquWrtW\
  rsWqrWoqWmpVloUmnUlmTklSjkShjRgiQfhQegPdfOceNbdNac\
  M`bL_aLY`KX_JWZJVXIUVHTTHSRGRQFQPFPNCWL9bJ6iH4oI4n\
  I4mJ5lK5jK5iL6hM6gM6eN6dO7cP7bP7`Q7_R8ZR8YS8WT9VT9\
  UU9TV9RVAQWAPXAOi9WXANLBF4sO4rO4rN4rN4rN4qM4qM4qM0\
  uN4qM8nLCkKFgKJdJNaIQYIUVHYSG`OGdLFhIEkEEoBDs8Cv5C\
  cUDNpBMqDMqEMqFLrGLrHLrILsJKsKKsLKtMJtOJtPZgaUhcPi\
  eLigMheNhdOgcPgbQfaRf`Se_TeZUdYVdXWcVXcUYbTZbS_aR`\
  aQa`Pb`Oc_Nd_MeZKfZJgYIhYHiXGjXFkWElWDmVCnVBq`5oY8\
  nVAmSCkP8lQElRJlRPlSUlSZmTdmUimUomVtmVyjXxhYxeZwc_\
  w``wZbvWcvUdvSeuPfuNhtKitIjtFksDlsCowBnuBmsAmrL7tO\
  6rS6pV5nZ4ma4ke3ih3gl2fo1ds1bv0`y0_AAaAFcAYeAhg9ki\
  8lf7mc7n`6oY6pV5qS4AP5AVFKJKkGPoHUwIaxGkyMpzUzzczz\
  mzzzzzzzzzzzzzzzzzzzzzzzz }

frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }

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