Cellular Automata get their Wires Crossed

TL;DR

This paper models two-dimensional cellular automata to demonstrate how communication channels can cross without interference, overcoming a fundamental limitation of 2D space by ensuring data capacity is maintained.

Contribution

It introduces a cellular automaton model that enables crossing of channels in 2D without data loss, providing a novel solution to a classic spatial communication problem.

Findings

Channels can be crossed without interference in 2D cellular automata

The system maintains data capacity during crossing

Potential applications in network design and computation

Abstract

In three spatial dimensions, communication channels are free to pass over or under each other so as to cross without intersecting; in two dimensions, assuming channels of strictly positive thickness, this is not the case. It is natural, then, to ask whether one can, in a suitable, two-dimensional model, cross two channels in such a way that each successfully conveys its data, in particular without the channels interfering at the intersection. We formalize this question by modelling channels as cellular automata, and answer it affirmatively by exhibiting systems whereby channels are crossed without compromising capacity. We consider the efficiency (in various senses) of these systems, and mention potential applications.