Lorentz attractor

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The Lorentz system of ordinary differential equations:

[math]\begin{aligned} \dot x &= \sigma (y - x) \\ \dot y &= x (\rho -z) - y \\ \dot z &= x y - \beta z \end{aligned}[/math]

exhbits chaos for certain parameters, for example [math]\sigma = 10, \beta = 8/3, \rho = 28[/math].

Its attractor (a curve in 3D space) has two spirals, with the curve transitioning between them unpredictably.

Original Page by Claude