Phase transitions in an elementary probabilistic cellular automaton with memory

Abstract

Standard cellular automata (CA) are ahistoric (memoryless): i.e., the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article considers an extension to the standard framework of CA by implementing memory capabilities in cells. Thus in CA with memory, while the update rules of the CA remain unaltered, historic memory of all past iterations is retained by featuring each cell by a summary of all its past states. A study is conducted of the effect of historic memory on a given side of the hypercube of elementary probabilistic CA which shows interesting phase transition phenomena.