Lorenz

Lorenz Attractor — Discovered by Edward Lorenz in 1963 while modeling atmospheric convection. The butterfly-shaped trajectory arises from a simplified system of three coupled differential equations. It was one of the first systems shown to exhibit deterministic chaos, where tiny differences in initial conditions lead to vastly different outcomes.

dx/dt = σ(y − x)
dy/dt = x(ρ − z) − y
dz/dt = xy − βz

Open Lorenz in chaosrack →

It opens running, on the model selector, with its own knobs. Rotate it by dragging, zoom with the wheel, and turn the parameters to see what the figure does when the system changes.