Coupled map lattices are spatially extended dynamical systems.
Local maps are positioned on the sites of a lattice and spatially coupled.
These can exhibit spatio-temporal chaotic behaviour.

If you just want to get a rough idea of what kind of complex behaviour is generated by coupled map lattices,
look at the following pictures.
They show the states of 1-dimensional diffusively coupled map lattices in space and time.
The colour at each pixel on the 100 X 100 lattice represents the value of an iterate of a local map
according to the following colour code:

red: value near to -1
yellow: value near to -0.2
green: value near to +0.2
blue: value near to +1

The horizontal direction is space, the vertical direction time.
In the various pictures the coupling strength between the local maps is varied.

If you would like to learn more on coupled map lattices and their physical applications,
you may look into this new book of mine.

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