Chaos While Sledding on a Bumpy Slope
This Demonstration shows two boards (or sleds) sliding down a mogul-infested hill. You can use the controls to see chaotic effects.
In the three snapshots, the two sleds follow the same general path on the hill with small moguls (0.45) (Snapshot 1) and on the hill with very large moguls (0.95) (Snapshot 3). In the intermediate case (mogul height of 0.6) (Snapshot 2), there is a clear case of divergence of paths, which is termed chaos. However, at the various mogul heights variation of the separation of the starting points can also lead to chaos. The text of the referenced book, The Essence of Chaos, is an excellent discussion of chaos, strange attractors, and other aspects of chaos. Of course, the icon of chaos was developed by Dr. Lorenz. The implementation of the sliding board by the author is found in R.M. Lurie, "A Review and Demonstration of 'The Essence of Chaos' by Edward N. Lorenz", Mathematica for Education and Research, 11(4), 2006 pp. 404–425.