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

TL;DR

This paper explores the mathematical relationship between one-dimensional cellular automata and integral value transformations, establishing their algebraic structures and applying IVTs to model DNA sequence evolution.

Contribution

It introduces a formal link between CA transition functions and IVTs, and develops their algebraic structures, also applying IVTs to DNA sequence evolution modeling.

Findings

Established algebraic structures for CA transition functions and IVTs

Linked CA and IVT models mathematically

Modeled DNA sequence evolution using IVTs

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.