## One-Dimensional Cellular Automaton Transitions and Integral Value Transformations Representing Deoxyribonucleic Acid Sequence Evolutions

Sreeya Ghosh
Electronics and Communications Sciences Unit, Indian Statistical Institute
Kolkata-700108, India
sreeya135@gmail.com

Sudhakar Sahoo
Institute of Mathematics and Applications
Bhubaneshwar-751029, India
sudhakar.sahoo@gmail.com

Sk. Sarif Hassan
Department of Mathematics, Pingla Thana Mahavidyalaya
Paschim Medinipur-721140, India
sksarifhassan@pinglacollege.ac.in

Jayanta Kumar Das
School of Medicine, Johns Hopkins University
MD-21287, USA
Applied Statistics Unit, Indian Statistical Institute
Kolkata-700108, India
dasjayantakumar89@gmail.com

Pabitra Pal Choudhury
Applied Statistics Unit, Indian Statistical Institute
Kolkata-700108, India
pabitrapalchoudhury@gmail.com

Antara Sengupta
Department of Computer Science and Engineering, University of Calcutta
Kolkata-700009, India
antara.sngpt@gmail.com

#### Abstract

The cellular automaton (CA) and an integral value transformation (IVT) evolving in discrete time steps are two mathematical models that are well established. Theoretically, it can be suggested that a CA possesses the capacity to produce varieties of evolutionary patterns. However, computing a CA in higher dimensions or computing a nonlinear CA may be complex. In such cases, an IVT can be conveniently used. This paper presents the relation between the transition functions of a one-dimensional CA and an IVT. It also highlights the algebraic structures on the basis of binary operations for a set of transition functions of a one-dimensional CA and for a set of IVTs. The suitability of using an IVT over a CA is discussed. Also, we present the evolutionary models of two deoxyribonucleic acid (DNA) sequences through IVTs and their spacetime diagrams. This can eventually bring out some characteristic features of the evolutionary sequences.

Keywords: CA; IVT; mutation and crossover operations; DNA sequence evolution

Cite this publication as:
S. Ghosh, S. Sahoo, Sk. S. Hassan, J. K. Das, P. P. Choudhury and A. Sengupta, “One-Dimensional Cellular Automaton Transitions and Integral Value Transformations Representing Deoxyribonucleic Acid Sequence Evolutions,” Complex Systems, 32(2), 2023 pp. 115–138.
https://doi.org/10.25088/ComplexSystems.32.2.115