Generalization of elementary cellular automata to a higher dimension family including the BML traffic model

TL;DR

This paper introduces a broad family of higher-dimensional cellular automata, including the BML traffic model, revealing new properties and behaviors through simulations, with applications across various scientific fields.

Contribution

It generalizes elementary cellular automata to higher dimensions, including the BML model, and uncovers new properties and applications through computational experiments.

Findings

Discovery of new properties of intermediate states in the BML model

Identification of sharp phase transitions and self-organization in new automata

Application of models to percolation, annealing, and biological membranes

Abstract

A general family of $D$-dimensional, $K$-state cellular automata is proposed where the update rule is sequentially applied in each dimension. This includes the Biham--Middleton--Levine traffic model, which is a 2D cellular automaton with 3 states. Using computer simulations, we discover new properties of intermediate states for the BML model. We present some new 2D, 3-state cellular automata belonging to this family with application to percolation, annealing, biological membranes, and more. Many of these models exhibit sharp phase transitions, self organization, and interesting patterns.