# What is a Mandelbrot Set Anyway?

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

*x*_{n+1}=

*x*

_{n}

^{2}+

*c*

*c*, is in the Mandelbrot set if, when starting with

*x*

_{0}=0 and applying the iteration repeatedly, the absolute value of

*x*

_{n}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; }

This specific example was found on http://llbb.wordpress.com/2007/04/12/mandelbrot-set-with-smooth-drawing-using-c/.
I'm looking for my original code that I used when studying Computer Science in high
school. But that was a long time ago. Once I find the original code, I'll
post an addendum.