Is the double pendulum chaotic — does a hair's-breadth difference in where you release it change everything?
▶ Launch the interactive simulationSwing a bright pendulum next to a faint ghost released δ=0.004 rad away (watch them split), and quantify it with a Benettin twin started δ₀=1e-8 away — renormalise the phase-space separation and average its log-growth into the largest Lyapunov exponent λ.
λ > 0 (exponential divergence ⇒ deterministic chaos / sensitive dependence) at large amplitude, vs λ ≈ 0 (two coupled normal modes) for a gentle release