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Monomial Cellular Automata: A number theoretical study on two-dimensional cellular automata in the von Neumann neighbourhood over commutative semigroups
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
2016 (engelsk)Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
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-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.

sted, utgiver, år, opplag, sider
2016. , s. 35
Emneord [en]
cellular automata, monomial, multiplicative, two-dimensional, von Neumann neighbourhood, number theory
HSV kategori
Identifikatorer
URN: urn:nbn:se:lnu:diva-51865OAI: oai:DiVA.org:lnu-51865DiVA, id: diva2:916251
Fag / kurs
Matematik/tillämpad matematik
Utdanningsprogram
Applied Mahtematics Programme, 180 credits
Presentation
2015-06-09, Växjö, 13:15 (engelsk)
Veileder
Examiner
Tilgjengelig fra: 2016-04-01 Laget: 2016-04-01 Sist oppdatert: 2016-04-01bibliografisk kontrollert

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Monomial Cellular Automata(2183 kB)110 nedlastinger
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