Boolean Network Attractors

Kauffman NK Random Boolean Networks & Attractor Landscape
6
2
0.50
N=6, K=2: ~√N attractors expected (ordered phase)

Kauffman NK Networks

K < 2: ordered phase — few attractors, long cycles

K = 2: critical (edge of chaos) — ~√N attractors, cycle length ~√N

K > 2: chaotic phase — exponentially many attractors

Each node has K random inputs and a random Boolean function. The 2^N state space collapses onto attractors (fixed points or limit cycles). At K=2 (Kauffman's "edge of chaos"), the number of attractors scales as √N — Kauffman proposed this models cell type diversity.