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According to Wikipedia... The Mandelbrot set is a set of points in the complex plane that 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 x2 + c remains bounded.
In something more closely approaching english.... If you plot real values on the X-axis and imaginary values on the Y-axis, the point X,Y is either inside (black) or outside the Mandelbrot set. You decide which by repeating a simple calculation based on the values of X & Y over and over again. The fun part is that the border between in and out never simplifies, no matter how closely you look.

Drag & drop the yellow square over any part of the border and you'll see what I mean. This dinky program gets slower and slower with every 10 fold amplification, so you may have to be patient... The software is built using only DHTML, the amazing thing is that it works at all.