; July 7, 1997: Point of Attraction 
;
; attraction
;
; 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\
  O8rN7wM5uM5rM5pM5nM6kN6iN6gN6dN6bN6`N7ZN7WN7UN7SN7\
  PO7NO8LO8IO8GO8007008008008318628938C48E59G69I79K8\
  9L99MA9NB9OC9PCAQDARDASDATDAUDAUEAUEBUEBUEBUEBVEBW\
  EBWEBXEBXEBYEBZECZEC_EC`EC`ECaDCbDCbDDcDDcCDdCDeCD\
  eCDfBDgBEgBEhAEiAEiAEjAEk9Ek9El9Fm8Fm8Fn8Fo8Fo7Fp7\
  Fp7Gq7Gr6Gr6Gs6Gt5Gt5Gu5Hv5Hv4Hw4Hx4Hy2Fy3Hx4Jx5Kx\
  6Mx7Ow8Qw9SwAUvCVvDXvEZuF`uGbuHduIetJgtKitLktMlsNm\
  rNmqOmqOnpPnoPnnQnnQnmRnlRokSokSojToiTohUogUpgVpfV\
  peWpdWpdXpcXqbYqaYq`Zq`Zq__qZ_rY`rY`rXarWarVbrVbsU\
  csTcsScsRdsRdtQetPetOftOftNgtMguLhuLhuKiuJiuIjuHjv\
  HkvGkvFlvElvEmvDmwCnwBnwAowAow9pw8px7qx7qx6rx5rx4s\
  x4sy3ty2ty2ty3sv4st4sr5ro5rm6rk6ri7rg7re8qb8q`9qZ9\
  qXAqVApSBpQBpOCpMCpKDpIDoFEoDEoBEp9Uq5Ur6Us8Ut9cuA\
  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===============================================
;