A connection between the percolation transition and the onset of chaos in the Kauffman model

Abstract

It is demonstrated numerically that the percolation transition of the unstable sites and the onset of chaos in the Kauffman model (1969) happens for the same value of the bias on the randomly chosen rules in the two-dimensional triangular lattice and in the three- and four-dimensional hypercubic lattices. The percolation thresholds for the stable sites are different for the three- and presumably also four-dimensional lattices. On the triangular lattice the differences between the thresholds are too small to be resolved. The fractal dimension of the damage is calculated and also the spreading time on the four-dimensional hypercubic lattice.