Complex Systems

Dynamics of Multicellular Automata with Unbounded Memory Download PDF

John W. Layman
Department of Mathematics,
Virginia Polytechnic Institute and State University,
Blacksburg, VA 24061-0123, USA


Cellular automata with unbounded memory, also known as mathematical neuron models or threshold automata, have been studied in the single-cell case by a number of authors. In this paper these automata are connected into multicelled networks and the dynamics of the resulting complex systems examined for certain neighborhood systems and interaction rules. Computer simulation and theoretical analysis are both presented. Some of the previously known properties of the dynamics of single cells persist in these systems, but many new properties appear. Most of these results pertain to networks of two or three cells with very simple forms of interaction between cells; however, there are also some implications for more general, larger systems.