; June 13, 1997: Galactic Supercluster
;
; supercluster
;
; Fractal visionaries:
;
; Every once in a while when I am exploring in the world of fractals, I
; make a major discovery that opens a whole new world of adventure.
; Today, while casually noodling around at lunchtime, I made one of those
; discoveries.
;
; Before putting my oblique plane formulas under wraps, I wanted to try a
; few things with them.  The first thing I did was to add a third variable
; to my Man-YZ-XZ formula, so that I could try different exponents of Z.
;
; The higher order mandeloids were uninteresting in the odd planes --
; squares instead of circles, but still uninteresting.  Then I tried
; Z^-2.  The results knocked my socks off.
;
; I discovered that the fractals drawn by the negative powers of Z, which
; are of limited interest in the Mandelbrot and Julia planes, are hiding
; their goodies in the other planes.  Here are all the spirals and whorls
; and seahorse tails that one would expect in a Mandelbrot fractal.  I've
; not yet found a midget, but I'm not sure if I'd recognize one even if I
; did find it.
;
; While the positive exponent Mandeloids become less interesting in the
; odd planes, the negative exponent mandeloids become more interesting.
; Now I've got another whole new world to explore.
;
; This is what keeps me going in the world of fractals -- even after eight
; years.  A serendipitous new approach, and the fractals I had virtually
; given up on have opened up and revealed . . . I don't know what.  But
; I'll be posting some Z^-2 images in the days to come.
;
; Today's fractal, Galactic Supercluster, is the first of the new -2
; world.  I've stretched it out in the vertical dimension to counter the
; tendency of the YZ plane to smear everything out horizontally.  The
; image has been posted to a.b.p.f. and a.f.p. for convenience.  And now
; I've got to get back to that -2 Mandeloid . . .
;
; Jim Muth
; jamth@mindspring.com
;
; START COMBINED FILE FOR 19.6===============================

Galactic_Superclus { ; time=0:00:16.80-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=ManN-YZ-XZ passes=1 center-mag=-2.8895\
  1188/+0.73347537/433.6914/0.04891/-0.283/-20.784
  params=0/0/-2/0/0/0 float=y maxiter=750 inside=253
  logmap=yes periodicity=10
  colors=0000000000000000000000000000000000000000000\
  00000000000000000000000000000000000000000000000000\
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}

frm:ManN-YZ-XZ {; Jim Muth, Thanks to Benno
  ; p3 = 0 = Julibrot YZ plane
  ; p3 = 1 = Julibrot XZ plane
  ; p3 = >0 <1 = Oblique planes
  z=real(pixel)+flip(real(p1)),
  c=imag(pixel)+flip(imag(p1)),
  a=p3, b=flip(cos(asin(p3))):
  z=z^p2+((a+b)*c),
  |z| <= 25
}

; END COMBINED FILE FOR 19.6=================================
;