Two Dimensional Discrete Dynamics of Integral Value Transformations

Das, Jayanta Kumar; Sahoo, Sudhakar; Hassan, Sk. Sarif; Choudhury, Pabitra Pal

doi:10.48550/arxiv.1709.05205

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2020

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“…The IVTs have been studied in different viewpoints including the understanding of the evolution of integer sequences and behavioral patterns of integers in discrete time points [14,15].…”

Section: Introductionmentioning

confidence: 99%

Relationship of Two Discrete Dynamical Models: One-dimensional Cellular Automata and Integral Value Transformations

Ghosh¹,

Sahoo²,

Hassan³

et al. 2020

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Cellular Automaton(CA) and an Integral Value Transformation(IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of evolution patterns. However computation of non-linear CA or higher dimensional CA maybe complex, whereas IVTs can be manipulated easily.The main purpose of this paper is to study the link between a transition function of a one-dimensional CA and IVTs.Mathematically, we have also established the algebraic structures of a set of transition functions of a one-dimensional CA as well as that of a set of IVTs using binary operations. Also DNA sequence evolution has been modeled using IVTs.

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“…The IVTs have been studied in different viewpoints including the understanding of the evolution of integer sequences and behavioral patterns of integers in discrete time points [14,15].…”

Section: Introductionmentioning

confidence: 99%