Dynamically generated Networks

TL;DR

This paper explores a class of complex networks generated by algebraic rules involving monoids and rings, linking them to dynamical systems and number theory, and illustrating their properties through various mathematical concepts.

Contribution

It introduces a novel class of networks generated by algebraic rules and connects them to multiple areas of mathematics, including dynamical systems and number theory.

Findings

Networks exhibit rich structures and complex patterns.

Connections to classical number theory problems like Fermat primes.

Elementary results related to the Chinese remainder theorem and Collatz problem.

Abstract

Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates this class of networks introduced together with Montasser Ghachem. Besides showing off pictures, we look at elementary results related to the Chinese remainder theorem, the Collatz problem, the Artin constant, Fermat primes and Pierpont primes.