A damped pendulum driven by a periodic force: θ'' + γθ' + sin θ = A cos(ωt). Stroboscopic sampling at the driving period reveals the Poincaré map. As drive amplitude A increases, the system transitions from regular orbits to a strange attractor — a fractal structure in phase space.
Poincaré section sampled every drive period T=2π/ω. Chaos boundary: A ≈ 1.066 (period doubling route). Strange attractor is a fractal with dim ≈ 2.0–2.3.