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8 Summary
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 Julia sets, we refer to the American
Mathematical Society volumes [10]
and [5].
References [3]
and [4]
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.
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