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Lorenz strange attractors

In 1963 the meteorologist and mathematician E. N. Lorenz published solutions for a simplified mathematical model of atmospheric turbulence in an air cell under a thunderhead. The model is now generally known as an illustration for chaotic behaviour and strange attractors.


Lorenz strange attractor

The basic equations are:


d(x1)/dt = a*(x2-x1)

d(x2)/dt = (r-x3)*x1-x2

d(x3)/dt = x1*x2-b*x3


  • x1 is the amplitude of the convective air currents
  • x2 is the temperature difference between the rising and falling currents
  • x3 is the deviation of temperature from the mean
  • a, r and b are dimensionless physical parameters

For more information, see

Download the model file and explore the behaviour of the strange attractor using Simile’s included XY-plotter, as set-up by this display configuration file.

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