20. Chaos

This very simple demonstration of a pendulum swinging above two magnets illustrates that Newton's laws do not always lead to predictable orderly motion. The pendulum bob is released from various initial positions, and it eventually comes to rest over one of the magnets, usually after undergoing complex irregular motion, often jumping from one magnet to the other. If you could accurately mark the release points for which the bob winds up over magnet one, you would find a "fractal" curve which is complex under any magnification. Points infinitesimally close to a point for which the bob winds up over magnet one will lead to the bob finishing over magnet two. It is not really practical to develop this curve in class, but the chaotic irregular motion of the bob is striking. This demo is suggested in Turning the World Inside Out by Robert Ehrlich (Princeton University Press 1990).

There is also a compound pendulum which shows chaotic motion (see Compound Chaotic Pendulum).