Pattern formation

Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour Social network analysis Small-world networks Centrality Motifs Graph theory Scaling Robustness Systems biology Dynamic networks Evolutionary computation Genetic algorithms Genetic programming Artificial life Machine learning Evolutionary developmental biology Artificial intelligence Evolutionary robotics Reaction–diffusion systems Partial differential equations Dissipative structures Percolation Cellular automata Spatial ecology Self-replication Conversation theory Entropy Feedback Goal-oriented Homeostasis Information theory Operationalization Second-order cybernetics Self-reference System dynamics Systems science Systems thinking Sensemaking Variety Ordinary differential equations Phase space Attractors Population dynamics Chaos Multistability Bifurcation Rational choice theory Bounded rationality The science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature.

Examples of pattern formation can be found in biology, physics, and science,[1] and can readily be simulated with computer graphics, as described in turn below.

[2] In developmental biology, pattern formation describes the mechanism by which initially equivalent cells in a developing tissue in an embryo assume complex forms and functions.

In industrial applications such as chemical reactors, pattern formation can lead to temperature hot spots which can reduce the yield or create hazardous safety problems such as a thermal runaway.

[20][22] Similarly as in chemical systems, patterns can develop in a weakly ionized plasma of a positive column of a glow discharge.

In such cases creation and annihilation of charged particles due to collisions of atoms corresponds to reactions in chemical systems.

[24][25] When a planar body of fluid under the influence of gravity is heated from below, Rayleigh-Bénard convection can form organized cells in hexagons or other shapes.

The interaction between rotation, gravity, and convection can cause planetary atmospheres to form patterns, as is seen in Saturn's hexagon and the Great Red Spot and stripes of Jupiter.

In the 1980s Lugiato and Lefever developed a model of light propagation in an optical cavity that results in pattern formation by the exploitation of nonlinear effects.

Computers are often used to simulate the biological, physical or chemical processes that lead to pattern formation, and they can display the results in a realistic way.

Pattern formation in a computational model of dendrite growth.
Tiger bush is a vegetation pattern that forms in arid conditions.
Pattern resembling a reaction–diffusion model, produced using sharpen and blur