The driven damped pendulum has multiple coexisting attractors. Their basins of attraction form fractal boundaries — regions of extreme sensitivity to initial conditions.
θ'' + γθ' + sin(θ) = A·cos(ωt). The pendulum can settle into different locked states depending on initial conditions (θ₀, θ'₀). Color encodes which attractor is reached. Near the fractal boundary, arbitrarily close initial conditions lead to different final states — the hallmark of fractal basin boundaries and the "uncertainty exponent" α = D − d_b.