Fractal visionaries:

We're entering the summer doldrums, (at least here in the northern hemisphere), and things are slowing down all around.  In honor of the occasion I've posted a hot fractal.  I named it "Dawning" because it vaguely reminds me of a sunrise.  But it looks like no sunrise I've ever seen on Earth.  Perhaps it's a sunrise on Mars.

Actually, it's a scene in a four-dimensional Mandelbrot set.  This is not the four-dimensional julibrot figure I talk about so much, but an actual 4-D Mandelbrot figure, where if the Julia sets are considered, we have an eight-dimensional figure.

No, I am not able to picture this object in my mind; I'm not even going to try.  The 4-D julibrot monster is hard enough.  But at least by taking that figure one 3-D slice at a time I'm making progress.

The formula is a slightly modified version of the Hypermandel formula in Fractint.  Being as obsessed as I am with the julibrot figure, I haven't done much exploring of the HyperSquare formula, but I do know that it's full of surprises.  Maybe one of these days I'll really dive down deep into it and find something entirely unexpected.

Today's image has been honorably posted to a.b.p.f. and a.f.p.  Tomorrow's fractal will be a surprise I found in the XZ plane.

Jim Muth
jamth@mindspring.com


START 19.6 FILE=============================================

Point_of_Atraction { ; time=0:00:56.24-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm
  formulaname=HyperSquare passes=t center-mag=+0.011\
  68689983424549/+0.1087448950599747/71.4165
  params=0/0.9993/10/0/1e-010/0 float=y maxiter=1600
  bailout=100 inside=0 logmap=yes periodicity=0
  colors=000O`LQ_KSZJVYIXXHZWG`VFcUEeTDgSCiRBlQAnP9p\
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  cvBcwDcxEhyFhzGhzImzJmzKmzLrzNrzOvzNvzcvzcvzczzczz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:HyperSquare {; Jim Muth
 a=(p1),b=(0,0):
  q=sqr(a)-sqr(b)+pixel
  b=p2*a*b+p3
  a=q,
   |a|+|b| <= 100 }

END 19.6 FILE===============================================