Mathematical experiments The first chapter introduces the basics of one-dimensional iterated maps. Take a function y = ƒ(x). Substitute some number into it. Take the answer and run it through the function again. Keep doing this forever. This is called iteration. The numbers generated exhibit three types of behavior: steady-state, periodic, and chaotic. In the 1970s, a whole new branch of mathematics arose from the simple experiments described in this chapter. Iteration Bifurcation Universality

Strange & complex The second chapter extends the idea of an iterated map into two dimensions, three dimensions, and complex numbers. This leads to the creation of mathematical monsters called fractals. A fractal is a geometric pattern exhibiting an infinite level of repeating, self-similar detail that can't be described with classical geometry. They are quite interesting to look at and have captured a lot of attention. This chapter describes the methods for constructing some of them. Strange attractors Julia sets Mandelbrot sets

About dimension The third chapter deals with some of the definitions and applications of the word dimension. A fractal is an object with a fractional dimension. Well, not exactly, but close enough for now. What does this mean? The answer lies in the many definitions of dimension. Euclidean dimension Topological dimension Fractal dimension