Okay, if we've survived through the first two labs we should have a much better feel for the concepts of phase-space, fixed points and stability of dynamical systems. However, we still haven't seen any chaos. As it turns out, I wasn't being nice, it just happens to be impossible to get chaos with less than three variables.
However, with three variables, things can get very interesting indeed. Here we will explore one of the classic systems that display chaotic behavior in three variables: the Lorenz Equations, which were explored (and explained) by Edward Lorenz in his phenomenal 1963 paper  ten years before Chaos was ``discovered''. Gleick  presents this story very nicely. Here we will delve into the quantitative aspects of chaos a bit more deeply using the tools we have already developed. When we are done I hope you will have a better understanding of