Two Lorenz attractors diverge from nearly identical initial conditions
The Lorenz system (1963) dx/dt=σ(y−x), dy/dt=x(ρ−z)−y, dz/dt=xy−βz exhibits sensitive dependence on initial conditions: two trajectories separated by ε diverge exponentially as e^(λt). The Lorenz attractor has a positive Lyapunov exponent λ≈0.906, making long-term prediction impossible — the butterfly effect.