Lorenz attractor

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Plot of a Lorenz attractor

The Lorenz attractor (also called Lorenz system) is a system of equations. Edward N. Lorenz formulated the equations as a simplified mathematical model for atmospheric convection. The equations are ordinary differential equations, called Lorenz equations. They are notable for having chaotic solutions for certain parameter values and starting conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.

The notion of butterfly effect is coupled with that of the Lorenz attractor. Lorenz first used the phrase in a speech he gave in 1972.

Lorenz Attractor Media

A sample solution in the Lorenz attractor when $ρ = 28$ , $σ = 10$ , and $β = 8 / 3$
Lorenz Ro14 20 41 20-200px
smaller Lorenz_Ro13.png
smaller Lorenz_Ro15.png
smaller Lorenz_Ro28.png
chaos in Lorenz attractor
chaos in Lorenz attractor
chaos in Lorenz attractor
Lorenz diverging trajectories small
Shows the map first created by Edward Lorenz which tracks the local maxima in z against the previous maximum, creating a map similar to the tent map. This image was created in Mathematica.
An animation showing trajectories of multiple solutions in a Lorenz system
An animation showing the divergence of nearby solutions to the Lorenz system