The Lorenz attractor is the icon of chaos theory: a fully deterministic system that is impossible to predict long-term. Tiny differences in starting conditions diverge exponentially — the famous butterfly effect.
Three coupled differential equations, derived by Edward Lorenz in 1963 to model atmospheric convection, produce trajectories that never repeat yet stay confined to a fractal butterfly-shaped attractor with dimension ≈ 2.06.
Drag to rotate the 3D attractor. Launch multiple particles with slightly different starting positions to visualise exponential divergence. Adjust ρ (rho), σ (sigma), and β (beta) to explore different attractor shapes.
Lorenz discovered chaos accidentally in 1961 by re-running a simulation with rounded values (0.506 instead of 0.506127). The forecast diverged completely, leading to his 1972 lecture asking whether a butterfly's wing-flap could trigger a tornado.