Visualizing the structure of chaos in the Lorenz system
The Lorenz attractor, with its characteristic butterfly shape, has become a much published symbol of chaos. It can be found by simply integrating almost any initial point. However, it is much more difficult to understand how the Lorenz attractor organizes the dynamics in a global way. We use a recently developed algorithm to compute a complicated two-dimensional surface called the stable manifold. Visualization tools are key to conveying its intricate geometry and beauty, which in turn provides insight into the structure of chaos in the Lorenz system.
chaos lorenz system strange attractor invariant manifolds