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\
  00000000000000000000000000000000000000000000000000\
  00000000000000000000000080070060050030020010000000\
  00000000000000000000000000000000000000000000000000\
  00000000000000000000000000000000000000000000000000\
  00000000000000000000000000000000000000000000000000\
  00000000000000000000000000000000000000000000000000\
  00000000000000000000000000000000000000000000000000\
  00000000000000000000000000000000000000000000000000\
  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===============================================