Here are some links to some great webpages on applying complex variables to explain the Mandelbrot and Julia sets.

The first is Mathworld's explanation of  the Mandelbrot Set and of the Julia Set

The second is Professor David Joyce's wonderful Mandelbrot Explorer, complete with a wonderful explanation section.

The third is John Hoggard's incredibly well-written site which explains Fractal Geometry with a link to some beautiful pictures of the Mandelbrot and Julia sets.

Here is another very clear description of the Mandelbrot set.

Other Websites Devoted to Complex Analysis

1. Tristan Needham's Visual Complex Analysis website list of links

2. Hans Lundmark's "Visualizing complex analytic functions using domain coloring"

Last Updated February 12, 2004