Chaos theory and Lorenz attractor

What was discovered

A system of three differential equations for atmospheric convection shows sensitive dependence on initial conditions and a strange attractor with a fractal structure. It established the limits of weather prediction (the butterfly effect).

The discovery arose from rounding a simulation's initial conditions to three decimal places.

What it led to

• chaos theory
• non-linear dynamical systems
• fractals
• ensemble forecasting in meteorology

Built on

• Poincaré (three-body problem)
• Smale (horseshoe map)
• digital computers

Made possible

• probabilistic weather forecasting
• chaotic encryption

📄 Original publication

Links