Lorenz Attractor

The Lorenz attractor is a well known system of three differential equations demonstrating deterministic chaos.  The model was originally derived by Edward Lorenz as an abstract description for convection rolls in the atmosphere, but is mainly studied for the insight it gives on the behavior of complex deterministic systems.

Download run the Matlab function LorenzDemo. Rotate and manipulate the resulting figure in phase space, and be sure you understand what is going on.  To test your understanding, modify this function to plot two trajectories on the same axis that start at nearby initial conditions, say less than 0.00001 apart. What happens to the trajectories over time?