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The Lorenz Attractor

The Lorenz System was the first recognized example of a chaotic dynamical system.

In Brief

Trajectories in the state space circle around one of two centers, switching between the two in an unpredictable, apparently random, but fully deterministic pattern.

Try It Yourself

To rotate the attractor, drag this slider.


In 1963 Edward Lorenz devised a simplified model of a single aspect (convection) of weather. The title of his paper, “Deterministic non-periodic flow,” captures the paradoxical nature of the solution to his equation. He discovered that changing the fourth-most significant digit in his starting value led to completely different long-term behavior.

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