Self-organization

Self-organization is the emergence of large-scale order from local interactions among components, without centralized direction. The resulting patterns can persist even as individual components change.

Positive feedback: A process in which a change amplifies itself through its effects. Local changes can recruit further activity, strengthening an emerging pattern.
Local interaction: An influence exchanged between nearby components in a system. Self-organization depends on component-level interactions rather than central instructions.
Bénard convection: A pattern of circulating fluid cells that can form when a fluid layer is heated from below. The cells emerge from thermal and fluid interactions rather than imposed circulation.
Centralized control: An arrangement in which a central authority directs the actions of subordinate components. It contrasts with patterns formed without a central directing authority.
Negative feedback: A process in which a change triggers effects that oppose or reduce it. It can limit growth and stabilize patterns formed through local interactions.
Distributed system: A system whose components act across multiple locations and coordinate through communication or interaction. Its organization is spread among components instead of concentrated in one controller.
Belousov–Zhabotinsky reaction: A chemical reaction that produces visible oscillations and traveling waves in concentrations of its reactants. Its chemical waves display organized dynamics generated by local reaction and diffusion.
Randomness: Unpredictable variation in outcomes or events, lacking a fixed deterministic pattern. Self-organized order can arise from interactions even when individual events include randomness.
Nonlinear dynamics: The study of systems whose outputs are not proportional to their inputs and whose behavior can depend sensitively on initial conditions. Nonlinear responses let small local interactions produce system-wide changes.
Collective behavior: Coordinated patterns of activity produced by interactions among multiple individuals or components. It describes the group-level coordination that self-organization can produce.

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