Fractal visionaries and enthusiasts:  

Today's image is a variation on a minibrot.  I named it "Minibrot Madness" because the minibrot is unlike any I have seen so far in Fractal Land.  Actually, the image is a continuation of the recent explorations in the 4-D HyperMandelbrot set created by hypercomplex numbers.

The 'stuff' condensing around the edges of the bays and buds of the minibrot is just as much a mystery as the eroded 'stuff' that obscures the minibrot in the image of March 04.  It has no right to be there, but there it is anyway, violating all the rules of common-sense math.

This 'stuff' is sensitive to the value of the real(p3) and real(p4) parameters.  And if the maxiter is increased, the 'stuff' expands and soon fills in the remaining open areas inside the minibrot.

The image might be a real fractal; it might be an artifact of math imprecision.  But until I find out exactly what is going on with these hyper-images, I will rate them with a question mark.

One thing not in doubt is the speed of the parameter file, which on the modern day speed-demons will finish in 45 seconds or less.  Of course, the simplest way to see the image is always to check it on one of the FOTD web sites.

Clouds and a temperature of 45F +7C prevailed today here at Fractal Central, while the fractal cat prevailed in my favorite chair.  The humans simply prevailed, which requires no further elaboration.

The next FOTD will be posted in the appropriate time.  Until whenever, take care, and they say heaven exists in four-dimensional space.  No wonder we can't spot it with our three-dimensional scientific devices.  All we can see are 3-D slices.

Jim Muth
jimmuth@earthlink.net


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

Minibrot_Madness   { ; time=0:00:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 center-mag=-0.7329986\
  40931621/+0.2212681808037857/4510/1/-158.75/0
  params=0/0/0/0/0.135/0/1e-070/0 float=y
  maxiter=2625 inside=0 logmap=-54 periodicity=0
  colors=000mtImtFltDjtAit8gvBcvD_wGWwISxLOxNKxPJtRI\
  pSHmTHiUGfVFbXE_YEWZDT_CP`COaEOZFQWHSTIURJVOLWLMYJ\
  OZGP`DQbBSd8Tg5Ui3Wj8YkD_lHamMcoQeoVgpZipckqgmrlor\
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  yy4yyEstOmoYgkgafqXboYdmYekYfiYhhZifZjdZlbZmaZn`Uo\
  _QoZMpYIpXDqW9qV5rU1rX3qZ5qa6qc8qf9qhBqkDqmEqpGqrH\
  qpJrnKrmLrkNrjOrhPrfQreSscTsbUs`VsZXsYYsWZsV_sYWn_\
  SjaOecKafGXhCTj8Ol4Kn0Gm3Em6Dm9CmCBmEAmH9mK8lN7lQ6\
  lS5lV4lY3l`2lc1le0hb4d_8`XCXUGTRKPPNLMRHJVDGZ9Db5B\
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  ZbE`cCbeAcf8Uk6Lo5Cs43w35t66q87nB8kDAhFBeICbK8eLD`\
  MHXMLSMPONTJNXFN`BNaHQbMTcRWdXZeaaffdBJZfegfkfRrqm\
  mlfpe_s_TvTNxNKnUIe`FWfDNm89yBEsEJnHNhKSczFJqKLmLO\
  iLReMUbMXZN_VNbROeNOhKPkOgYN0UN0UEB0NAAWAKdAUmAanG\
  dnMfoRioXkpbmpgpqmrzzzzzz }

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