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.

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Remarks

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.