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July 6, 1997: Obscured Blue Bud July 5 July 7 1997 FOTD Home

bluebud

Fractal visionaries:

Today's fractal is a scene in one of the "perturbed" Mandelbrot planes.  This scene is parallel to the classic Mandelbrot set but off to one side of it.  It shows a bud, (or radical as Mandelbrot calls them), nearly buried but still clearly visible through a foreground haze of low iteration clutter.

I was truly amazed when I discovered that these elusive ghost buds exist in the background of many routine perturbed scenes, ready to be revealed by a high maxiter and proper coloring -- almost as though the low-iteration and high-iteration ranges were doing entirely different things.

These perturbed remnants of the classic M-set are always found at the same coordinates at which they are found in the classic set.  If the perturbed scene is not obscured by low iteration clutter, a ghostly remnant of the true set will always be present in the high-iteration range, and this remnant remains fixed in place regardless of the starting point of the perturbed set in which it appears.

The fact that these high-iteration remnants remain fixed in position through a wide range of starting points is the reason that the horizontal high-iteration bands appear in the XZ, XW, YZ and YW planes.  Those horizontal bands are parts of the classic set viewed at a right angle.  Their straightness indicates that they do not move when the starting point is changed.

The picture itself is an attempt to capture a feeling of illumination from within, as though a source of light were just off the screen.  It is only moderately effective due to the limitation of the banding and the 256 colors.  When true color arrives, this effect will be much easier to achieve.

Today's image is posted on alt.binaries.pictures.fractals and alt.fractals.pictures.  Tomorrow is Monday.  That means back to work and a new and better fractal.  Keep posted.

Jim Muth
jamth@mindspring.com


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

Obscured_Blue_Bud  { ; time=0:01:59.35-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm
  formulaname=Mandelbrot passes=1 center-mag=+0.2150\
  729627720058/+0.5346985111755886/350.3348
  params=0.456/0.654/100/0 float=y maxiter=15000
  inside=253 periodicity=10 ranges=0/-1/330/420/560\
  /750/950/1350/1850/2550/5000/15000 sound=off
  colors=000A00UA00QS0bc0hf0ke0vdhumwwwzzzzzz0000000\
  00000KKKOOOSSSWWW___ccchhhmmmssszzz00zG0zW0zj0zz0z\
  z0jz0Wz0Gz00zG0zW0zj0zz0jz0Wz0Gz00z00zG0zW0zj0zz0j\
  z0Wz0GzVVzbVzjVzrVzzVzzVrzVjzVbzVVzbVzjVzrVzzVrzVj\
  zVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhzmhzqhzvhzzhzzhvzhq\
  zhmzhhzmhzqhzvhzzhvzhqzhmzhhzhhzmhzqhzvhzzhuzhqzhl\
  z00S70SE0SL0SS0SS0LS0ES07S00S70SE0SL0SS0LS0ES07S00\
  S00S70SE0SL0SS0LS0ES07SEESIESLESPESSESSEPSELSEISEE\
  SIESLESPESSEPSELSEISEESEESIESLESPESSEOSELSEHSKKSMK\
  SOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKSSKQSKOSKMSKKSKKSMK\
  SOKSQKSSKQSKOSKMS00G40G80GC0GG0GG0CG08G04G00G40G80\
  GC0GG0CG08G04G00G00G40G80GC0GG0CG08G04G88GA8GC8GE8\
  GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8CG8AG88G88GA8GC8GE8\
  GG8EG8CG8AGBBGCBGEBGFBGGBGGBFGBDGBCGBBGCBGEBGFBGGB\
  FGBDGBCGBBGBBGCBGEBGFBGGBFGBDGBCGUdfU0MU6QTCUTIYTO\
  `SUdS_h00e0e00eeKKme0eeL0 }

frm:Mandelbrot {; Jim Muth
z=p1, c=pixel:
z=sqr(z)+c,
|z| <=p2 }

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