One of the most remarkable mathematical developments of the twentieth century was the understanding of what has become known as chaos. Nonlinear differential equations of order three or higher can show a behaviour that appears almost random, even though the equations are deterministic. Trajectories can diverge from each other exponentially, but thanks to a kind of repeated folding action, the solutions remain in a finite region of phase space. These solutions are described as chaotic. Chaos is difficult to analyse in differential equations, but it is much simpler to study and understand in discrete systems, or difference equations, which are closely related to differential equations.