Emergence

Emergence is the appearance of large-scale properties or patterns from interactions among smaller components. Those properties are not straightforwardly present in the components considered separately.

Self-organization: The spontaneous formation of organized structure through interactions among a system’s components. It describes how local interactions can produce ordered patterns without a central organizer.
Reductionism: The approach of explaining complex phenomena through the properties and interactions of their simpler components. Emergent explanations often retain component-level causes while stressing that they do not tell the whole story.
Weak emergence: Emergence in which system-level behavior follows from lower-level rules but may be difficult to predict without simulation. It captures novelty and unpredictability without denying that component rules generate the outcome.
Conway's Game of Life: A cellular automaton whose simple rules generate patterns with complex behavior. Its moving structures and self-replicating patterns emerge from local cell updates.
Predictability: The degree to which a system’s future behavior can be inferred from its present state and governing rules. Emergent outcomes may follow from rules yet remain practically unpredictable.
Feedback: A process in which a system’s outputs influence its subsequent inputs or behavior. Feedback can amplify or dampen local changes, shaping system-level patterns.
Micro–macro link: The relation between a system’s small-scale components and its large-scale properties. Emergence concerns how descriptions at these different scales connect.
Strong emergence: The proposed existence of higher-level properties or causal powers not reducible to lower-level physical processes. It makes a stronger claim about irreducibility than ordinary complex-system explanations require.
Ant colony: A social insect colony whose members coordinate through interactions and environmental cues. Collective foraging and nest behavior arise without a colony-wide plan.
Computational irreducibility: The idea that some computations have no shortcut and must be run to determine their outcomes. It offers one account of why simple rules can yield outcomes that resist prediction.

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