3D animation of the Lorenz Attractor trajectory, implemented in Python using the 4th order Runge-Kutta method.

The Lorenz attractor is a set of chaotic solutions to a system of ordinary differential equations called the Lorenz system. First studied by Edward Lorenz with the help of Ellen Fetter, who developed a simplified mathematical model for atmospheric convection. The model is a system of three ODEs:

The state variables are x, y and z. The rate at which states are changing is denoted by dx/dt, dy/dt and dz/dt respectively. The constants σ, ρ and β are the physical parameters.