Self-organized criticality

Self-organized criticality is a property of slowly driven, dissipative systems that evolve toward a critical state and produce events across a wide range of sizes without external tuning.

Bak–Tang–Wiesenfeld sandpile: A cellular automaton in which slowly added grains trigger avalanches when local height thresholds are exceeded. This model first demonstrated how repeated driving and dissipation can produce avalanches of many sizes.
Slow driving: Input applied on a timescale much longer than the system’s internal relaxation time. Separated timescales let activity subside between additions in classic SOC models.
Forest-fire model: A cellular automaton in which trees grow and lightning ignites fires that spread to neighboring trees. Its fire-size statistics offer a simple model of driven, cascading events.
Equilibrium critical point: A point in a system’s phase diagram where distinct phases meet and critical fluctuations emerge. Unlike SOC, an equilibrium critical point generally requires tuning external parameters.
Per Bak: A Danish physicist whose work helped establish the theory of self-organized criticality. Bak developed the concept with Tang and Wiesenfeld and later promoted its broad applications.
Avalanche (self-organized criticality): A cascading event in which local changes propagate through a system until activity stops. Avalanches are the characteristic events whose size distribution signals critical behavior.
Dissipation: The irreversible loss or dispersal of energy from a system. Dissipation prevents indefinitely accumulating input and helps set the system’s evolving state.
Olami–Feder–Christensen model: A nonconservative earthquake model in which stress redistribution triggers cascades of failures. It applies SOC ideas to fault-like systems while varying how much stress is dissipated.
Percolation theory: The mathematical study of connected clusters formed by randomly occupied sites or bonds. Percolation can generate power laws at a tuned threshold without slow driving or dissipation.
Chao Tang: A physicist who co-authored the 1987 paper introducing the sandpile model of self-organized criticality. Tang’s collaboration supplied the original model with Bak and Wiesenfeld.

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