Emergent Properties in Structurally Dynamic Disordered Cellular Networks

TL;DR

This paper explores the properties of dynamic cellular networks modeling space-time at the Planck scale, analyzing their large-scale behavior, phase transitions, and network dimension to understand potential continuum limits.

Contribution

It introduces a novel connection between dynamic cellular networks and SDCA, emphasizing non-linear interactions to emulate fluctuating space-time structures.

Findings

Network dimension behavior in large-scale limits

Evidence of phase transitions in models

Insights into continuum limit prospects

Abstract

We relate structurally dynamic cellular networks, a class of models we developed in fundamental space-time physics, to SDCA, introduced some time ago by Ilachinski and Halpern. We emphasize the crucial property of a non-linear interaction of network geometry with the matter degrees of freedom in order to emulate the supposedly highly erratic and strongly fluctuating space-time structure on the Planck scale. We then embark on a detailed numerical analysis of various large scale characteristics of several classes of models in order to understand what will happen if some sort of macroscopic or continuum limit is performed. Of particular relevance in this context is a notion of network dimension and its behavior in this limit. Furthermore, the possibility of phase transitions is discussed.