There are any number of sites on the World Wide Web dedicated to galleries of computer-generated fractal images. Pictures based on Lyapunov Exponent fractals, such as the one pictured above, are some of the most striking and unusual.
Like most fractal images, Lyapunov Exponent fractals are produced by iterating functions and observing the chaotic behaviour that may result.
In this article, we'll be exploring what Lyapunov exponents are, how you iterate functions, what "chaos" really is, and how you go about turning simple maths into marvellous images. There's also a companion article, Computing the Mandelbrot set by Andrew Williams, which looks at the technical details involved in writing a program to compute the Mandelbrot set.