Coupled Map Lattices

A time evolution plot of a one dimensional coupled map lattice with periodic boundary, where the map is x_n+1 = a+x_n/(b + x_n²). The time axis goes from left to right, and the lattice sites go from bottom to top. The color indicates the value of the map residing at that lattice point. 

Simple maps like the logistic map x = r x_n(1 - x_n) can have complicated one dimensional dynamics. When two or more unimodal maps are coupled together we get an extended system with complex dynamics, such as the system pictured above. Even though the individual maps in the above picture are operating in a chaotic region of their parameter plane, there is more apparent order to their coupled evolution than there is in a single chaotic map.