Correspondence between neural threshold networks and Kauffman Boolean cellular automata

For an asymmetric version of the McCulloch-Pitts neural network (1943) and for Kauffman's infinite-range Boolean network model (1984), the time evolution of the Hamming distances between two different initial configurations are compared in the thermodynamic limit. It is shown that in both models phase transitions occur for corresponding values of the transition parameters and that their Hamming distances can have the same time evolution leading to quantitatively the same dynamics, as known from time-dependent Landau theory for phase transitions.