One of the earliest indications of chaotic behavior was in an atmospheric model developed by Edward Norton Lorenz. His goal was to describe the motion of a fluid layer that is heated from below. The result is convection, where warm fluid at the bottom rises, then cools at the top, and finally descends as a result. Lorenz simplified the description by restricting the motion to two spatial dimensions. This situation has been observed in the laboratory and is known as a Rayleigh-Bénard cell.

In the equations below, the dimensionless parameters $\sigma$, $\rho$, and $\beta$ are determined by various fluid properties, the size of the Rayleigh-Bénard cell, as well as the temperature difference in the cell. (In the program, $\rho$ = `r`

and $\beta$ = `b`

). Note that the variables $x$, $y$, and $z$ have nothing to do with actual spatial coordinates, but are instead simply convenient measures of the state of the system. This exercise is meant to reinforce the idea that even simple sets of equations can exhibit chaotic behavior.