Let’s try the odex JavaScript library in the browser to explore the Lorenz strange attractor:

Move the mouse around the graph to perturb the initial conditions a bit. (Slower is better, to watch the dynamics shift.) You can see the sensitive dependence on initial conditions as the imaginary point decides which of the two lobes to hang around in and how long to stay there!

These solutions of the Lorenz equations are projected into the -plane.