Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure
arXiv:2406.15408 · doi:10.1007/978-3-031-71552-5_5
Abstract
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is that this modification not always goes in the sense of decreasing the entropy.
arXiv commentThis is a rather different paper with respect to the first version (which appeared in the proceeding of ACRI 2024): it includes results about the Hopfield model and should be a different preprint, but arxiv policies forbade it