Asynchronism in Cellular Automata

TL;DR

This paper introduces Skewed Fully Asynchronous Cellular Automata (SACA), analyzing their dynamics and demonstrating their effectiveness in solving clustering problems with faster convergence and efficiency.

Contribution

The study presents a novel asynchronous update scheme for cellular automata and explores its theoretical properties and practical applications in clustering.

Findings

ECAs exhibit diverse behaviors under SACA, including reversibility and divergence.

Lattice size divisibility influences system dynamics and atomicity effects.

Reversible asynchronous CA effectively solve clustering problems with rapid convergence.

Abstract

This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step. The behavior and dynamics of elementary cellular automata (ECA) under this scheme are analyzed and compared with those of synchronous and fully asynchronous update methods. The comparative analysis highlights a range of phenomena, including transitions in ECAs from convergent or non-reversible dynamics to reversible, divergent behavior. The divisibility of lattice size by 2 or 4 is shown to have significant effects on the system dynamics, linked to the presence or absence of atomicity. The study also explores the convergence of ECAs to all-zero or all-one point attractors under SACA, providing theoretical insights that align with experimental findings. Additionally, the research investigates the application of fully asynchronous cellular automata in solving clustering problems. Clustering is defined as grouping objects with similar properties. The proposed method employs reversible asynchronous cellular automata to merge clusters iteratively based on their closeness, continuing until the desired number of clusters is achieved. This approach leverages a small set of rules, leading to faster convergence and efficiency in clustering tasks. The findings underscore the potential of asynchronous cellular automata as a versatile and effective framework for studying complex system dynamics and solving practical problems such as clustering.