Elementary Cellular Automata with Memory

Abstract

Standard cellular automata (CA) are ahistoric (memoryless), that is, the new state of a cell depends on the neighborhood configuration of only the preceding time step. This article introduces an extension to the standard framework of CA by considering automata with memory capabilities. While the update rules of the CA remain unaltered, a history of all past iterations is incorporated into each cell by a weighted mean of all its past states. The historic weighting is defined by a geometric series of coefficients based on a memory factor (alpha). A study is made of the effect of historic memory on the spatio-temporal and difference patterns of elementary (one-dimensional, two states, nearest neighbors) CA starting with states assigned at random.