Newsgroups: alt.binaries.pictures.fractals
From: mrob@world.std.com (Robert P Munafo)
Subject: - mm6.gif (0/2)
Organization: The World Public Access UNIX, Brookline, MA
Date: Fri, 22 Oct 1993 05:42:53 GMT

	mm6.gif is a uuencoded picture of an island mu-molecule at the
center of a second-order imbedded Julia set.  The image was rendered
on a Macintosh, using my own software.  The color mapping was done
in HLS (hue-luminance-saturation) space.  The distance-estimator algorithm
was used for the luminance, and the iteration count was used for the
other two compnents.  The formulas used are:

    hue = 10 * log(its) / log(MAX_ITS)
    sat = (1.0 - 0.5 * log(its) / log(MAX_ITS)) * (1 + (its MOD 2)) / 2
    lum = { 1.0, if distance > 1.0
          { 1.0, if distance = 0.0
          { 0.0, if distance < 1.0e-10
          { 0.5 * (1.0 - (log(distance) / log(1.0e-10)))  otherwise
 
In the hue formula, "10" is used to create a total of 10 rainbows.
Only the fraction counts, i.e. a hue of 2.5 is the same as a hue of
0.5.  0.0 is red, 0.33 is green, 0.67 is blue, etc.

In the luminance calculation, the "distance" is assumed to be
in *pixel* units, which means you have to take the result of the
distance estimator formula and divide by the pixel spacing for the
current view size and resolution.
 
The original image is in 24 bits per pixel, but I performed
Floyd-Steinberg dithering to make an 8-bit image suitable for
turning into a GIF.

The coordinates are shown in the image itself.  The line which reads
"RF(1/2B1)FS[3/7B1][0][0]{[2]}x7J16" is the name in my custom naming
system for features of the Mandelbrot Set; the name refers to the
mu-molecule (island) along with all of the filaments out to the
edge of the pink region.