Fractals such as the dragon above can be generated through a number of methods. They can also arise when modelling realistic systems. In this essay I give an overview of how how complicated behaviour can evolve out of the solution of a basic system such as the driven pendulum as well as through the application of simple mappings of sets. Some understanding of differential equations and set theory is assumed. The essay is an updated copy of one submitted for a course in Topology and Chaos, lectured by Professor Sid Morris at the University of Wollongong in October of 1996.