Lorenz attractor

Three equations from a toy model of convection. The path never repeats and never settles, looping round one wing, then the other, in an order no one can predict far ahead. The lit stretch is the present; the faint loops are its past.

ẋ = σ(y − x), ẏ = x(ρ − z) − y, ż = xy − βz; σ = 10, ρ = 28, β = 8/3

On mathcurve.com as Attracteur de Lorenz