Internet Explorer just crashed on me! I now have to rewrite this.
I've gotta build
Live Writer support
into my site one of these days. Anyway...
A Mandelbrot Set is a fractal. It is a complex formula based image (more
on that in a moment). You pass values to define scale. Wikipedia defines
a Mandelbrot Set as (because I can't for the life of me remember the *real* definition)
a set of
points in
the
complex
plane, the
boundary of
which forms a
fractal.
Mathematically, the Mandelbrot set can be defined as the set of complex
c-values
for which the
orbit of
0 under
iteration of
the
complex
quadratic polynomial
xn+1 = xn2 + c
remains
bounded.
A Complex number,
c, is in the Mandelbrot set if, when starting with
x0=0
and applying the iteration repeatedly, the
absolute
value of
xn never exceeds a certain number (that
number depends on
c) however large
n gets.
Yeeeeaaaah. Exactly. Talk about a pain to remember. I prefer
to remember the code definition:
Math.ComplexNumber C = z;
int iteration
= 0; while (z.Modulus < escapeRadius && iteration
< maxIteration) { z = z * z + C; iteration++; } int colorIndex
= 0; if (iteration < maxIteration) { z = z * z + C; iteration++;
z = z * z + C; iteration++; double mu = iteration - (Math.Log(Math.Log(z.Modulus)))
/ logEscapeRadius; colorIndex = (int)(mu / maxIteration
* 768); if (colorIndex >= 768) colorIndex = 0; if (colorIndex
< 0) colorIndex = 0; }