Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 55, Issue 35, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac8382
Keywords
cellular automata; reversibility; replication; budding
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This article reports on the replication of arbitrary patterns by reversible and additive cellular automata, providing an explicit description of the orbit and replication process under specific conditions.
In this article, the replication of arbitrary patterns by reversible and additive cellular automata is reported. The orbit of an 1D cellular automaton operating on p symbols that is both additive and reversible is explicitly given in terms of coefficients that appear in the theory of Gegenbauer polynomials. It is shown that if p is an odd prime, the pattern formed after (p - 1)/2 time steps from any arbitrary initial condition (spatially confined to a region of side less than p) replicates after p + (p - 1)/2 time steps in a way that resembles budding in biological systems.
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