Lorenz system: ẋ=σ(y−x), ẏ=x(ρ−z)−y, ż=xy−βz. Nearby trajectories (shown as color cloud) diverge exponentially. The Lyapunov exponent λ₁>0 quantifies chaos. Kaplan-Yorke dimension D_KY = 2 + λ₁/(λ₁+|λ₃|).