Strange Repeller — Hamiltonian Chaos

In a Hamiltonian system with escaping trajectories, the set of initial conditions that never escape forms a fractal called the strange repeller. Here we use the Hénon-Heiles potential — originally modeling stellar orbits — and color each point by how quickly its trajectory escapes to infinity. The fractal structure at the basin boundary reveals the repeller.

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Hénon-Heiles: H = ½(ẋ²+ẏ²+x²+y²) + x²y − y³/3  |  Escape condition: r > 1
Color = escape time. Black = trapped (on the repeller). Fractal boundary = chaos.
Click to zoom into a region.