---
tag: 77JZ2QRZ4M
kind: concept
name: Coupled map lattice
msc: [37L60, 37N20]
specializes: [BBZP1R872N]
sources:
  - url: https://en.wikipedia.org/wiki/Coupled_map_lattice
same_as:
  wikidata: Q5178018
  wikipedia: Coupled map lattice
---

## Summary

A coupled map lattice is a [[dynamical system|BBZP1R872N]] with discrete time, discrete space and continuous state.
At each site of a lattice sits a real variable.
It is updated by a nonlinear map such as the [[logistic map|QN9X9BNKTX]] and then mixed with the values at neighbouring sites.
Coupled map lattices were introduced by Kunihiko Kaneko in the 1980s as simple models of spatiotemporal chaos, turbulence and pattern formation.
They show a rich variety of behaviour, such as frozen patterns, travelling defects and fully developed spatiotemporal chaos.

## Explanations

### L1 human

Think of a row of cells, each holding a number.
At every tick of a clock, each cell first applies the same simple rule to its own number, and then averages a little with its two neighbours.
With a chaotic rule, each cell alone would behave erratically; the coupling makes the whole row form patterns that move, merge and break up.
It is a toy model for systems like a turbulent fluid, where chaos happens in space as well as in time.