e show that a class of deterministic lattice gases with discrete Boolean elements simulates the Navier-Stokes equation, and can be used to design simple, massively parallel computing machines.

We study some simple dissipative dynamical systems exhibiting a transition from a stable periodic behavior to a chaotic one. At that transition, the inverse coherence time grows continuously from zero due to the random occurrence of widely separated bursts in the time record.

Kauffman's model is a random complex automata where nodes are randomly assembled. Each node o, receives K inputs from K randomly chosen nodes and the values of Q? at time t + 1 is a random Boolean function of the K inputs at time t. Numerical simulations have shown that the behaviour of this model is very different for K > 2 and K S 2. It is the purpose of this work to give a simple annealed approximation which predicts K = 2 as the critical value of K. This approximation gives also quantitative predictions for distances between iterated configurations. These predictions agree rather well with the numerical simulations. A possible way of improving this annealed approximation is proposed.

No abstract

No abstract