July 6, 1997: Obscured Blue Bud | July 5 | July 7 | 1997 | FOTD Home |
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\
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z0jz0Wz0Gz00zG0zW0zj0zz0jz0Wz0Gz00z00zG0zW0zj0zz0j\
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zhmzhhzmhzqhzvhzzhvzhqzhmzhhzhhzmhzqhzvhzzhuzhqzhl\
z00S70SE0SL0SS0SS0LS0ES07S00S70SE0SL0SS0LS0ES07S00\
S00S70SE0SL0SS0LS0ES07SEESIESLESPESSESSEPSELSEISEE\
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`SUdS_h00e0e00eeKKme0eeL0 }
frm:Mandelbrot {; Jim Muth
z=p1, c=pixel:
z=sqr(z)+c,
|z| <=p2 }
END 19.6 FILE===============================================