Relationship of Two Discrete Dynamical Models: One-dimensional Cellular Automata and Integral Value Transformations
Cellular Automata and Lattice Gases
2020-07-01 v2 Discrete Mathematics
Dynamical Systems
Abstract
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 modelled using IVTs.
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Cite
@article{arxiv.2006.13741,
title = {Relationship of Two Discrete Dynamical Models: One-dimensional Cellular Automata and Integral Value Transformations},
author = {Sreeya Ghosh and Sudhakar Sahoo and Sk. Sarif Hassan and Jayanta Kumar Das and Pabitra Pal Choudhury},
journal= {arXiv preprint arXiv:2006.13741},
year = {2020}
}
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20 Pages