Physical implementation of asynchronous cellular automata networks: mathematical models and preliminary experimental results

Abstract

Physical implementation of asynchronous cellular automata networks has shown stably random oscillations under certain conditions. We present two simple mathematical models to describe transient and stationary regimes. The models are based on simple assumptions taking into account several aspects such as number of inputs of the cellular automata, rule balance, and technological frequency limitation. Numerical simulations reveal the possibility of chaotic dynamics of the average transition rate of the cellular automata in a stationary regime. With physical implementations on FPGA (field programmable gate array), preliminary experimental results show very good qualitative agreement with model’s prediction and numerical simulations. Several networks of interconnected 5-input asynchronous cellular automata have been successfully implemented in different FPGA devices, and we present some preliminary experimental results. This work aims at finding fundamental mechanisms of randomness such that the collective behavior of the cellular automata system does not depend on physical implementation details.