Thus, the Mandelbrot set possesses an extraordinary amount of structure. We can use the geometry of M to understand the dynamics of x2 + c. Or we can take dynamical information and use it to understand the shape of M. This interplay between dynamics and geometry is on the one hand fascinating and, on the other, still not completely understood. Much of this interplay has been catalogued in recent years by mathematicians such as Douady, Hubbard, Yoccoz, McMullen, and others, but much more remains to be discovered.
For more details on the Mandelbrot and filled Julia sets, we refer to the American Mathematical Society volumes  and . References  and  contain more general referencs to the theory of dynamical systems. The Mandelbrot Set Explorer is a new, web-based interactive approach to many of the topics contained herein.