Phase diagram, the Lorenz attractor
Fig 2. Attractors highlight stable regions
Visualising complex systems
The Lorenz attractor has become an emblem of chaos theory. The equations were first derived by a meteorologist, Ed Lorenz, in 1963 to represent a simplified model of the earth’s convection system. The 3 non-linear equations are:
The graphic produced by the equations is actually a 3-dimensional graph, although typically we can only visualise a 2-dimensional representation through flat media. The system demonstrates extreme sensitivity to initial conditions and never repeats itself. As can be seen in the above figure, when plotted the system oscillates between two steady states (known as attractors), although, like the weather, it never converges into a steady state.