Asynchronism in Cellular Automata
Virendra Kumar Gautam

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…
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Taxonomy
TopicsCellular Automata and Applications
