Chaos theory and the Mandelbrot set : an honors thesis (HONRS 499)

Abstract

In this thesis I study two main ideas: Chaos Theory and the Mandelbrot Set. Chaos Theory is a relatively new field of science that is revolutionizing the way we look at predictability and randomness. The Mandelbrot Set is a spectacular image generated by looking at a somewhat universal class of functions. First, I give a brief history of Chaos Theory, looking at three people who helped develop it. Then, for the second part of this thesis, I explore the mathematics behind the Mandelbrot set and explain some interesting properties of it, in particular, the regions corresponding to fixed points, two-, and three-cycles. I conclude by stating two theories about the set that have not been able to be proven mathematically.