Self-organized criticality¶
Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of 1/f noise. Physical Review Letters, 59(4), 381-384.
Cited by¶
6 citations across 6 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Cascade
- The pattern was first studied quantitatively in physical and biochemical systems — nuclear chain reactions, where each fission liberates neutrons that induce further fissions, and enzymatic signaling chains, where one activated molecule activates many copies of the next — and it was given a general mathematical home in percolation theory and the science of self-organized criticality, where the question becomes whether a local flip dies out or sweeps the lattice.
This sourceIntroduces self-organized criticality via the sandpile cellular automaton, giving cascades a general mathematical home and modeling avalanche/fracture-like systems poised at the boundary between sub- and super-critical propagation.
- The pattern was first studied quantitatively in physical and biochemical systems — nuclear chain reactions, where each fission liberates neutrons that induce further fissions, and enzymatic signaling chains, where one activated molecule activates many copies of the next — and it was given a general mathematical home in percolation theory and the science of self-organized criticality, where the question becomes whether a local flip dies out or sweeps the lattice.
- Criticality
- Criticality is structurally distinct from the threshold at which the transition occurs (a scalar control-parameter value) and from the transition event itself: criticality is the regime in which the system lives at or near that boundary, with its distinctive statistical fingerprints, and it can be sustained indefinitely when endogenous dynamics tune the system toward the boundary, as Bak, Tang, and Wiesenfeld (1987) demonstrated with the sandpile model.
This sourceIntroduces self-organized criticality via the sandpile cellular automaton, showing that endogenous slow-driving/dissipation dynamics keep a system at the boundary between sub- and super-critical propagation with power-law avalanche statistics—the prime's 'sustained indefinitely' claim.
- Criticality is structurally distinct from the threshold at which the transition occurs (a scalar control-parameter value) and from the transition event itself: criticality is the regime in which the system lives at or near that boundary, with its distinctive statistical fingerprints, and it can be sustained indefinitely when endogenous dynamics tune the system toward the boundary, as Bak, Tang, and Wiesenfeld (1987) demonstrated with the sandpile model.
- Scale Invariance
- - T4 — Mechanisms Are Multiple and Non- Unique: Many mechanisms produce power- law distributions (preferential attachment, random multiplicative processes, self-organized criticality
This sourceSelf-organized criticality as mechanism generating scale-invariant power-law distributions without external tuning.
- - T4 — Mechanisms Are Multiple and Non- Unique: Many mechanisms produce power- law distributions (preferential attachment, random multiplicative processes, self-organized criticality
- Self-Organization
- Bak, Tang, and Wiesenfeld (1987) demonstrated self-organized criticality: systems with many interacting units can self-tune to critical thresholds (power-law distributions, scale-free dynamics) through feedback, exemplifying how complexity arises without explicit tuning
This sourceIntroduces self-organized criticality via the sandpile cellular automaton, giving cascades a general mathematical home and modeling avalanche/fracture-like systems poised at the boundary between sub- and super-critical propagation.
- Bak, Tang, and Wiesenfeld (1987) demonstrated self-organized criticality: systems with many interacting units can self-tune to critical thresholds (power-law distributions, scale-free dynamics) through feedback, exemplifying how complexity arises without explicit tuning
- Threshold-Driven Order Emergence
- T2 — Nucleation engineering vs. nucleation suppression. For desired orderings (consensus, innovation, adoption), nucleation is valuable and can be engineered.
This sourceIntroduces self-organized criticality via the sandpile cellular automaton, giving cascades a general mathematical home and modeling avalanche/fracture-like systems poised at the boundary between sub- and super-critical propagation.
- T2 — Nucleation engineering vs. nucleation suppression. For desired orderings (consensus, innovation, adoption), nucleation is valuable and can be engineered.
- Universality in Critical Phenomena
- T3 — Universality Can Be Broken by Quenched Disorder, Long-Range Interactions, or Non-Equilibrium Driving:
This sourceIntroduces self-organized criticality via the sandpile cellular automaton, giving cascades a general mathematical home and modeling avalanche/fracture-like systems poised at the boundary between sub- and super-critical propagation.
- T3 — Universality Can Be Broken by Quenched Disorder, Long-Range Interactions, or Non-Equilibrium Driving:
Verification¶
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