N nodes, K inputs each — tune K to find the phase transition between order and chaos
Network state (time flows down)
Hamming distance (two nearby states)
Phase: Critical (K=2)
Kauffman's NK model: N binary nodes, each with K random inputs and a random Boolean lookup table.
K=1: frozen (ordered) — perturbations die out. K=2: critical edge of chaos — attractor cycles ≈ √N.
K≥3: chaotic — tiny differences in initial state grow exponentially (positive Lyapunov exponent).
The Hamming distance between two nearby trajectories reveals the phase: decreasing = ordered, growing = chaotic.