Lorenz (1963) simplified convection: ẋ=σ(y−x), ẏ=x(ρ−z)−y, ż=xy−βz.
Classic: σ=10, ρ=28, β=8/3 → strange attractor. Two trajectories start 10⁻⁸ apart — they diverge exponentially
(Lyapunov exponent λ₁≈0.906). This makes weather prediction fundamentally limited: errors double every ~1.1 days.
The butterfly effect: not just sensitivity, but topology. The attractor is fractal, dimension ≈2.06.