Abstract
This paper is a brief treatment of some areas of complex dynamics. It
will treat the area of Julia Sets and the Mandelbrot Set. This subject is
rich in content, and therefore only a small part of this area will be
explored. It was not possible to include all parts of this subject in
this paper that the author wanted. The main areas which will be covered are some
historical background and basic definitions, several escape criterion and
how they lead to an algorithm for drawing the Julia Set, the Fundamental
Dichotomy, and several interesting areas such as exploding Julia Sets.