One-dimensional cellular automata with memory:: Patterns from a single site seed

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 introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remain the same, each site remembers 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). The time evolution of one-dimensional CA with memory starting with a single live cell is studied. It is found that for alpha less than or equal to 0.5, the evolution corresponds to the standard (nonweighted) one, while for alpha > 0.5, there is a gradual decrease in the width of the evolving pattern, apart from discontinuities which sometimes may occur for certain rules and alphavalues.