On the dynamics of stochastic elementary cellular automata

In this paper the dynamics of stochastic elementary cellular automata (SECAs) is investigated and compared to that of their deterministic counterparts. We observe that moving away from the determinism in von Neumann's original design impacts CA dynamics to such an extent that sensitive dependence on initial conditions might get lost abruptly, or also the other way around, might arise suddenly. As such, the behavior in a deterministic setting can be unrepresentative for the dynamics one gets in a stochastic setting. In the case of SECAs, it turns out that the involved probabilities should be understood as bifurcation parameters steering the nature of such SECAs, i.e. whether or not they are unstable.

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