CLOUDS IN THE BASINS OF FULLY ASYNCHRONOUS CELLULAR AUTOMATA

Abstract

This paper studies the basins of attraction of fully asynchronous cellular automata (ACAs) that converge to point attractor. Unlike traditional (synchronous) cellular automata (CAs), an ACA may approach to different point attractors from the same initial condition for different runs. In this direction, this paper introduces the notion of cloud behavior in convergence dynamics of ACAs. Depending on the cloud behavior, we classify the convergent ACAs into three classes—eccentric cloud, partially eccentric cloud and deterministic cloud system. In addition, this study observes the computational ability of addressing density classification problem (i.e. distributed consensus problem) of this asynchronous cloud system.