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.
Supported in partVerified against the publisher's abstract
Its abstract states that systems with spatial degrees of freedom evolve to a self-organized critical point — the self-organized-criticality half of the claim's mathematical-home clause.
“We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point.”
- 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.
Supported in partVerified against the publisher's abstract
Abstract supports systems evolving into a self-organized critical point and 1/f noise as critical-state dynamics, but not the sandpile or 'sustained indefinitely' details.
“We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state.”
- 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.
Supported in partVerified against the publisher's abstract
The abstract backs self-organized criticality as a mechanism generating scale-invariant 1/f behaviour, but it speaks of 1/f noise and fractal objects, not of 'power-law distributions'.
“We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state. This picture also yields insight into the origin of fractal objects.”
- - 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.
Supported in partVerified against the publisher's abstract
The abstract states that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point; it supports the self-tuning half of the claim but not the power-law, scale-free or feedback clauses.
“We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state.”
- 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¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 4 of 6 citations: 4 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:e0e6ebcac465 · see in the full table