Fractal visionaries and enthusiasts:  

Today's image is a scene in the eastern part of the main bud of the HyperMandelbrot set, just west of Seahorse Valley.  I posted it as a FOTD because of its interesting repeating patterns, which almost but not quite repeat identically.

The image rates a 7.5 and would have rated higher if similar near-repeating patterns were not so plentiful in the classic Mandelbrot set.

The name "8-Dimensional Landscape" indicates that the image is a slice of the 4-dimensional HyperMandelbrot set, which itself is a 4-D slice through the center of the 8-D HyperJulibrot figure.

I am beginning to make some sense of these hyper images, but I still have a long way to go before everything adds up.

The calculation time of 2-1/4 minutes borders on slowness.  The web sites can bring relief however.

Today brought thick clouds then heavy snow to Fractal Central, while the temperature hovered just at freezing.  As of post time, about 2 inches (5cm) had piled up.  The fractal cat took a quick glance out the shelf window, then settled to sleep.  The humans spent the day getting the routine things done.

The next FOTD will be posted in a reasonable time.  Until reason prevails, take care, and take time to think things out.

Jim Muth
jimmuth@earthlink.net


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

8-Dimens_Landscape { ; time=0:02:15.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1 float=y
  center-mag=-0.7978139292256579/-0.016458707578773\
  58/2177/1/-157.5/0 params=0/0/0/0/0.5/0/1e-018/0
  maxiter=750 inside=0 logmap=-358 periodicity=0
  colors=000UYWOQcMO`LNYKMWJLTIKRHJOGIMCXG8kB4z62tN1\
  ob3qc5rd6te8uf9wgBxhCyhFxZHxPJxFLqDNjBPc9QX7SQ5UJ3\
  VC2OI8INECSK6XQUYXpZbkafgdjcgmZjqVmuRoxXhsbaogVjmO\
  fsHaxAYqH`kNbeTe__gUejOglTinYgg_caU`iNbpG`wIZpKUiM\
  QcOLXQHRSCKT8EUDDVICWNBXRAYW9Z`8_d7`eD`eJaePaeVbe`\
  befcblaaqZbjUadP_ZLYTGWNBUH6SB2Q5I`6Yj6mt6ghDaXKWL\
  RR9XZCVeFTlIRsLPmRSgXVabYWg_VQVV8R_C_cFghIplLxpFqr\
  Ajp5dm6Tj7HcBDZF7TL7OT8PX9Q`ARaASXBSKCNFBI9AJ4AJ8A\
  L9ANAAPBARCATDAVEAXFFYFL_FN`FPaFRbLTcQVdWXe`ZadWfg\
  _kkcpoguokznnvkktfhrZepSboOanL_nOVoRUoULeUUXObNIkI\
  GoEDsFJnFOiFTdFY`FdWFiREoQFjNGbLHTJIJHI9FLFEOKERQE\
  UVEX`E_eEXr2ajEkbUecQ`cNWcKQcHLcEGcBBc8H`7MZ7SX7XU\
  6bS6gQ6fR8eSAdSCcTEhWHbTFXRDSOCMMAHJ9BH76F6KJ5XN4j\
  R3wV2oS6hPAaMEVJINGMGDQ9AU27Y8HXERXK`WQjWUrRVsWVt_\
  VudWvhWwmWxqWyu_vvcsvfqvjnvnkvqivpewpaxpYxpUypQzpN\
  zmQtjTohWjeZeHnJca`jHOyPr }

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=========================================