Lorenz Attractor

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The Lorenz attractor is a simplified model of convection of a gas within a confined space. This very simple model results in some very interesting motion, an example of deterministic chaos. A chaotic system is very sensitive to initial conditions and the system rapidly diverges.

The system is described by three coupled non-linear differential equations:

dx / dt = a (y - x)
dy / dt = x (b - z) - y
dz / dt = xy - cz

where

  • a is the *Prandtl number* representing ratio of fluid viscosity to thermal conductivity
  • b is the *Rayleigh number* representing the difference in temperature between the top and bottom of the box
  • c is the ratio of the width to height of the box.

Commonly used constants are a = 10, b = 28 and c = 8/3.