The Butterfly Effect and Chaos Theory

Edward Lorenz discovered in 1961 that tiny changes in initial conditions could drastically alter weather predictions – the ‘butterfly effect’. His Lorenz system dx/dt = σ(y – x), dy/dt = x(ρ – z) – y, dz/dt = xy – βz has a strange attractor: a fractal of dimension ≈ 2.06. The system is deterministic but unpredictable beyond a finite time horizon (sensitive dependence). This is chaos. The butterfly effect became a cultural icon, but the mathematics (Lyapunov exponents) is rigorous. Chaos appears in heart rhythms, lasers, and even the solar system.