Fractal visionaries and enthusiasts:  

Today's image lies in the hyper stuff filling an unresolved filament in the East Valley area of yesterday's image.  Its name is "The Big Break-Up", which does not refer to a failed love relationship, (sorry ladies) but rather to the two arms at the center of the image that have broken off from the other four.

The image is actually a two-dimensional slice through the four-dimensional HyperMandelbrot set.  And this 4-D HyperMandelbrot set is a 4-D slice through its parent eight-dimensional Julibrot.  I'll make no effort to describe things possible in 8-D space; It's hard enough to describe things in 4-D space.  But one thing certain is that:

         8 lines
         28 planes
         56 3-spaces
         70 4-spaces
         56 5-spaces
         28 6-spaces
         8 7-spaces

pass through every point in 8-D space.

Not surprisingly, this series of numbers appears in Pascal's Triangle, as do many other interesting number series.

Down to this point, the near circular hyper-holes have had six broad arms converging toward their centers.  But in today's image, two of these arms, the two on the right, are breaking away from the main mass, and from here on down there are only four arms converging on the centers of the holes.  Will two more arms break away somewhere down in the bottomless depths and leave us with only two converging arms?  I have no idea, but the number of arms remains at four as far as the Fractint program can take us.

As far as I can see, there is too little art in the image for a rating above an everyday average 5.  The math aspect is far more interesting however, and rates an 8.

The calculation time of 1-1/3 minutes is fast enough to prevent impatience, but the task of setting up and running the included parameter file remains unsolved.  The web sites will solve this situation.

Snow began at daybreak here at Fractal Central today, and continued at a moderate rate all morning, piling up to about 5 inches or 13cm by the time it ended in the afternoon.  The fractal cats were amused by the falling snow for an hour or so, then kept themselves busy by chasing each other up and down the hallway.  The humans were in work mode in the morning, but we shifted to snow-clearing mode in the afternoon.

The next FOTD will be posted shortly.  To see how shortly, check back here at frequent intervals.  Until this big fractal event happens, take care, and when someone claims that matter is the ultimate reality, I don't mind; and when someone else claims that mind is the ultimate reality, it doesn't matter.

Jim Muth
jimmuth@earthlink.net


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

The_Big_Break-Up   { ; time=0:01:20.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 center-mag=-0.7544388\
  80647367/+0.05254690385569359/5.8041e+010/1/58.25/0
  params=0/0/0/0/0.5/0/1e-100/0 inside=0 maxiter=1310
  float=y logmap=1052 periodicity=0 mathtolerance=0/1
  colors=0004AX5BW6CU8DSAEQCFOEGMGFKJEIODGTCEYBCcAAr\
  u0qt0ps0nr0mq0lp0jo6inAhmEelIbiM_fQXcUV`XSY_PVbMRe\
  JOhHLkEInBFq8Ct69w9BuBDsDFqFHoHJmJKlLMjNOhQQfSSdUT\
  cWVaYX__ZYa`_caddcieemfgqghtgjwhlzimzjozjqzkrzltzz\
  vzzwzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzSCQ`KNiTKr`HmbLic\
  OdeR`fUXhXSi_OkbKleImaGnYEoUCpQAqM8rI7rEEsBKt9Qt7W\
  u5au3enDigNmaWqVeuOoxIxU5EiCXyJoqQjjWeca`WgWPmRIsM\
  PRZRWcS_hUcmVgrQjlLmfHp`NiYSbWYXTbQRhKOmDMr7Kj_Jkb\
  IleHmhGnjFomEppDqsCquBmpFjlJghNddQ`_UYWYVSaSOdZTid\
  YmjbqpguvlyweswZnxSixLdYfgXbdW_bVW_TSXSPVRLSQHPPEN\
  OAKN6HM3FL6IL9LLCNLFQLISLLVKOXKR_KUaKXdK_fKbiKdkOe\
  iSfhWgg_hfcidgjckkbolamm_lmZjmXimWgmVfmTdmScmRbnP`\
  nO_nMYnLXnKVnIUnHTnGyE1xG4wI7vKAuLCtNFsPIrQKqSNpUQ\
  oVSfPNYKIQFDPDEOCFNBGMAHL9IK8JK7KJ6LI5MH4NG3OF2PF1\
  QH5TI8WJBZKEaLHdMKgNNitWK }

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