Rendering the Mandelbrot Set.

The usual algorithm for computing pictures of the Mandelbrot set actually computes a function of its complement. When used to picture the Mandelbrot set itself the results are rather poor. I describe an algorithm for accurately rendering the Mandelbrot set that produces, for example, connected pictures - this is appropriate since the set itself is connected. The algorithm is based upon a result of Thurston on the distance from the Mandelbrot set to a point in its complement. I also show how this idea may be extended to hyperbolic components of the set.