Pattern Formation
First published: 2008
Brief summary
Scholarpedia overview of pattern formation across systems.
Article
Pattern formation is the emergence of organised spatial or temporal structure from an initially more uniform state. It occurs in systems such as fluids, chemical reactions, biological tissues, neural activity and ecological populations.
Instability is often the first step. A small disturbance grows when local positive feedback amplifies it, while transport, inhibition, depletion or boundary conditions limit the growth and determine the spacing and shape of the resulting pattern.
Reaction–diffusion models describe interacting substances that react locally and spread through space at different rates. Other mechanisms include convection, mechanical stress, phase separation, wave propagation and coupling among oscillating units.
Mathematical analysis identifies the conditions under which a uniform state becomes unstable and which spatial modes grow fastest. Experiments and observations are then required to determine whether the proposed variables and interactions correspond to the mechanism operating in a particular system.
Source details and credits
- Source / publisher: Scholarpedia
- Source type: Reference article
- URL type: WWW
- Credits: Scholarpedia
- URL: http://www.scholarpedia.org/article/Pattern_formation