The Mathematica Programmer

Function Iteration and Chaos

Volume 5, Issue 2
Spring 1995

We present a number of programs to investigate and visualize chaos as it occurs with iterated application of functions. We look at ways to picture orbits under repeated application and to draw final-state diagrams. We discuss symbolic and numerical methods to find periodic orbits, bifurcation points, super-attractive orbits, and the Feigenbaum constant. Further topics include statistical analysis and visualization of chaotic phenomena such as sensitivity, mixing, ergodic orbits, and intermittency.