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Monomial Cellular Automata: A number theoretical study on two-dimensional cellular automata in the von Neumann neighbourhood over commutative semigroups
Linnaeus University, Faculty of Technology, Department of Mathematics.
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this report, we present some of the results achieved by investigating two-dimensional monomial cellular automata modulo m, where m is a non-zero positive integer. Throughout the experiments, we work with the von Neumann neighbourhood and apply the same local rule based on modular multiplication. The purpose of the study is to examine the behaviour of these cellular automata in three different environments, (i.e. the infinite plane, the finite plane and the torus), by means of elementary number theory. We notice how the distance between each pair of cells with state 0 influences the evolution of the automaton and the convergence of its configurations. Similar impact is perceived when the cells attain the values of Euler's-$\phi$function or of integers with common divisors with m, when m > 2. Alongside with the states of the cells, the evolution of the automaton, as well as the convergence of its configurations, are also decided by the values attributed to m, whether it is a prime, a prime power or a multiple of primes and/or prime powers.

2016. , p. 35
Keywords [en]
cellular automata, monomial, multiplicative, two-dimensional, von Neumann neighbourhood, number theory
Mathematics
Identifiers
OAI: oai:DiVA.org:lnu-51865DiVA, id: diva2:916251
Educational program
Applied Mahtematics Programme, 180 credits
Presentation
2015-06-09, Växjö, 13:15 (English)
Examiners
Available from: 2016-04-01 Created: 2016-04-01 Last updated: 2016-04-01Bibliographically approved

Open Access in DiVA

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Cite
Citation style
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