; July 23, 1997: Spire 
;
; spire
;
; Fractal visionaries:
;
; In yesterday's posting, I mentioned that iterated points of the
; Mandelbrot plane, no matter where they start, unless they escape first,
; will eventually settle into the same orbits as the points that start at
; 0,0.  This tendency of points to converge on the same orbits is the
; cause of the high-iteration horizontal bands in the odd planes of the
; julibrot.  In the Mandelbrot planes this tendency to converge creates
; ghost images of the true set in the high-iteration background of the
; perturbed sets.  Today's fractal takes advantage of this phenomenon.
;
; I named the scene "Spire" because of the prominent green spire that
; points right.  The purplish low-iteration parts in the foreground
; converge on the greenish background of high-iteration remnants.  In this
; case, the image is part of the "true" set.  The greenish background is
; the ghost of an even more true set that doesn't exist in the 0,0
; Mandelbrot plane.
;
; The formula mixes parts of the Z^2 and Z^3 Mandelbrot sets.  The mixture
; warps the entire julibrot figure, pulling the "true" part of the
; Mandelbrot aspect away from the 0,0 plane.  One of these days I'm going
; to hunt up the "truer" set, and see that green background in its
; unobscured glory.
;
; Today's image is posted on a.b.p.f. and a.f.p.  Tomorrow I'll have
; another great, (IMHO), fractal, and I'll explain my technique for
; getting today's coloring effects.
;
; Jim Muth
; jamth@mindspring.com
;
; START 19.6 FILE=============================================

Spire              { ; time=0:00:27.08-SF5 on P4-2000
  reset=2004 type=formula formulafile=jim.frm
  formulaname=ObliqueMixPlus passes=t
  center-mag=-0.66879/-0.211436/3.031269/1/85/0
  params=0/0/-4.159/0.103/0/0.3 float=y maxiter=1500
  inside=253 periodicity=10 ranges=0/-1/100/110/125\
  /150/200/300/450/650/900/1200/1500 sound=off
  colors=000gKZIAK0XPK`PPdPUgPanSisZqvZzzzzzzzzz0000\
  00000000000000000000000000000000000000000000000000\
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  00000000000000000000000080070060050030020010000000\
  00000000000000000000000000000000000000000000000000\
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  00000000000000000000000000000000000000000000000000\
  00000000000000000000000002C02C02C02C03C03C03C03C03\
  C03C03C04D04D04D04D04D04D04D05D05D05D05D0000000000\
  00011011011011011011012012022022022022023023023033\
  03303303303403403403404404404504504504504504505605\
  605605606307000300G000000
}

frm:ObliqueMixPlus {;Jim Muth
  z=(p1+pixel), c=p2+(p3*pixel):
  z=sqr(z)+(0.2*(z*z*z))+c,
  |z| <=100
}

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