The stadium billiard (two semicircles + rectangle) is a paradigm of chaotic billiards — proved ergodic by Bunimovich (1979). Unlike circular or elliptic billiards (integrable), nearby trajectories diverge exponentially. Click inside the stadium to launch a trajectory from that point. Watch the Poincaré section fill ergodically.
Click canvas to add trajectory from that point. Stadium: two semicircles of radius 1, rectangle width a.