A billiard ball bouncing between circular obstacles — exponential sensitivity and fractal escape basins
Click on the billiard to launch a particle. Chaos emerges from a circular obstacle.
Sinai billiard (Ya. Sinai, 1963): A square table with a circular scatterer. Despite deterministic dynamics, nearby trajectories diverge exponentially — the hallmark of chaos. Lyapunov exponent λ > 0. The escape time map (right) shows fractal structure: initial conditions are partitioned into infinitely thin strips of similar escape time, separated by stable/unstable manifolds. This is the simplest ergodic billiard, and a model for Boltzmann's ergodic hypothesis. Click the arena to launch trajectories.