Complex Systems: Self-organization

A system displays self-organization when its components spontaneously arrange themselves in spatial or temporal patterns through processes often triggered by internal random fluctuations amplified by positive feedback loops. Typical self-organized systems in physics and biology are thermodynamic systems permanently driven out of equilibrium, but many other examples abound:

• crystallization
• convection patterns in fluid flow
• swarming of animals
• pattern formation
• morphogenesis in plants and animals, etc.

An important special form of self-organization is self-organized criticality, where self-organization gets combined with critical behavior. Criticality is typically exhibited by systems undergoing a phase transition, e.g., water going through its freezing or boiling points. At these critical points the medium changes suddenly and discontinuously from one qualitative state to another (e.g., from liquid to solid in the freezing of water). In self-organized criticality a system’s dynamics spontaneously tunes itself to a critical point. The paradigm example of this phenomenon is Per Bak’s self-organizing sand pile (see references).