Direct Counting Analysis on Network Generated by Discrete Dynamics

TL;DR

This paper investigates the in-degree distribution of cellular automata networks through exact enumeration and transfer matrix methods, revealing deviations from multiscaling and size dependence for certain rules.

Contribution

It introduces a detailed enumeration approach and transfer matrix augmentation to analyze in-degree distributions in cellular automata networks, including size dependence insights.

Findings

Large deviation from multiscaling in ID

Distribution dependence on lattice size for some rules

Method extends to complex cellular automata rules

Abstract

A detail study on the In-degree Distribution (ID) of Cellular Automata is obtained by exact enumeration. The results indicate large deviation from multiscaling and classification according to ID are discussed. We further augment the transfer matrix as such the distributions for more complicated rules are obtained. Dependence of In-degree Distribution on the lattice size have also been found for some rules including R50 and R77.