---
tag: RM94KBV8P7
kind: concept
name: Turing pattern
msc: [35B36, 35K57, 92C15]
sources:
  - url: https://en.wikipedia.org/wiki/Turing_pattern
same_as:
  wikidata: Q56273850
  wikipedia: Turing pattern
---

## Summary

A Turing pattern is a stationary, spatially periodic pattern that forms in a [[reaction–diffusion system|TAAHWE917M]] from an instability caused by diffusion.
Alan Turing described the mechanism in 1952 in "The Chemical Basis of Morphogenesis".
The surprise is that diffusion, which usually smooths out differences, can destabilise a uniform state when two substances diffuse at different rates.
Turing patterns are proposed as explanations of spots and stripes in animal coats and other biological patterns.

## Explanations

### L1 human

Think of an activator that makes more of itself and of an inhibitor, and suppose the inhibitor spreads much faster.
A small local excess of activator grows, but the inhibitor it produces spreads around it and stops growth nearby.
The result is a regular arrangement of peaks with a typical spacing, such as spots or stripes.
Without diffusion the mixture would stay uniform; the difference in diffusion rates is what creates the pattern.