Cellular Automata Rules and Linear Numbers
Birendra Kumar Nayak, Sudhakar Sahoo, Sagarika Biswal
TL;DR
This paper explores the recursive generation of linear cellular automata rules using a binary tree, introduces the concept of linear numbers associated with these rules, and investigates their mathematical properties.
Contribution
It presents a novel recursive method for generating linear CA rules and defines linear numbers, analyzing their properties for the first time.
Findings
Linear CA rules can be generated recursively using a binary tree.
Linear numbers associated with CA rules have specific mathematical properties.
The paper derives new results on both linear and non-linear CA rules.
Abstract
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
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Taxonomy
TopicsCellular Automata and Applications · DNA and Biological Computing · Advanced Data Storage Technologies