Edge of chaos

The edge of chaos is a regime near the boundary between ordered and chaotic dynamics. Some complex systems in this regime display complex patterns, long-range correlations, and flexible information processing.

Dynamical system: A system whose state changes over time according to specified rules. The edge of chaos describes a regime within a system’s possible dynamics.
Deterministic system: A system whose future state is fixed by its current state and governing rules. Deterministic rules can generate both orderly motion and chaos.
Cellular automaton: A grid of discrete cells that update their states according to local rules. Changing a cellular automaton’s rules can produce ordered, chaotic, or intermediate patterns.
Fixed point: A state of a dynamical system that remains unchanged under its evolution rule. Fixed points represent a limiting form of orderly behavior.
Self-organized criticality: A proposed tendency for driven, dissipative systems to evolve toward critical states without fine-tuning. It offers a distinct route to critical dynamics that may resemble edge-of-chaos behavior.
Bifurcation: A qualitative change in a system’s behavior as a parameter crosses a threshold. Bifurcations can mark transitions from ordered behavior toward chaos.
Chaos theory: The study of nonlinear systems whose behavior is highly sensitive to initial conditions. The edge of chaos is defined in relation to chaotic dynamics.
Conway's Game of Life: A cellular automaton on a square grid whose cells follow four simple birth-and-survival rules. Its complex structures illustrate how local rules can support organized computation.
Limit cycle: An isolated periodic orbit toward which nearby trajectories converge or from which they diverge. A limit cycle is regular and repeating, unlike dynamics at the boundary.
Critical brain hypothesis: The proposal that neural activity operates near a critical point between distinct dynamical regimes. It applies related criticality claims to brain activity and information processing.

Linked from 1 page

Dambisa MoyoBroader topic: It applies her policy critique to the institutions and incentives of democratic governance.