Lorenz System
In 1963 Edward Lorenz introduced a simple 3-variable model for convection in the atmosphere. The model consists of the 3 first-order nonlinear differential equations shown below. For some parameter values the solutions of these equations are chaotic. This suggests why long-term daily weather forecasts are not possible.
The video shows phase-space behavior of an analog computer for the Lorenz system. The analog computer was constructed one night in the lab by Jarrett Lancaster, one of our physics majors, just for fun because it was interesting.