Kauffman NK Network: Edge of Chaos

Kauffman's NK model connects N nodes in a random Boolean network, each receiving K inputs and computing a random Boolean function.

The phase transition at K=2 (for p=0.5) is the "edge of chaos" — Derrida's mean-field analysis predicts λ = 2Kp(1−p).

λ < 1 → frozen (perturbations die). λ > 1 → chaotic (perturbations spread). λ = 1 → critical.

The Derrida plot shows how an initial overlap between two states evolves — critical networks have the diagonal as a fixed point.