THE FIRST famous chaotic system discovered by Edward Lorenz corresponds exactly to a water wheel -- a simple device that proves capable of surprisingly complicated behavior.

Water pours in from the top at a steady rate. If the flow of water is slow, the top bucket never fills up enough to overcome friction, and the wheel never starts turning. If the flow is faster, the weight of the top bucket sets the wheel in motion {left}. The wheel can settle into a rotation that continues at a steady rate {center}.

But if the flow is faster still {right}, the spin can become chaotic because of the nonlinear effects built into the system. As buckets pass under the flowing water, how much they fill depends on the speed of spin. If the wheel is spinning rapidly, the buckets have little time to fill up and can start up the other side before they have time to empty. As a result, heavy buckets on the side moving upward can cause the spin to slow down and then reverse.

In fact, Lorenz discovered, over long periods, the spin can reverse itself many times, never settling down to a steady rate and never repeating itself in any predictable pattern.