Cellular Automata with Memory

Ramón Alonso-Sanz & Margarita Martín

Universidad Politécnica de Madrid

Standard cellular automata (CA) are ahistoric (memoryless): that is, the new state of a cell depends on the neighborhood configuration only at the preceding time step: σ_i^(T + 1)=φ(σ_j^(T)N_i).

This contribution considers an extension to the standard framework of CA by implementing memory capabilities in cells. Thus in CA with memory here, while the update rules of the CA remain unaltered, historic memory of all past iterations is retained by featuring each cell (and link) by a summary of its past states: σ_i^(T + 1)=φ(s_j^(T)N_i), with s_j^(T)=s(σ_j^(1),…,σ_j^(T - 1),σ_j^(T)).

The effect of memory on different types of CA as well as on other discrete dynamical systems is assessed in this work.

[presentation materials]

Created by Mathematica  (May 11, 2006)