Transmitting-state invertible cellular automata

TL;DR

This paper introduces a new method for constructing invertible cellular automata based on the concept of cells transmitting or receiving information exclusively, and explores an example with conserved energy.

Contribution

It generalizes existing approaches by proposing a transmission-based rule construction for invertible cellular automata.

Findings

New class of invertible cellular automata rules introduced

Example with additive conserved energy analyzed

Potential applications in modeling reversible physical systems

Abstract

Invertible cellular automata are useful as models of physical systems with microscopically revesible dyanmics. There are several well-understood ways to construct them: partitioning rules, second-order rules, and alternating-grid rules. We present another way (a generalization of the alternating-grid approach), based on the idea that a cell may either transmit information to its neighbors or receive information from its neighbors, but not both at the same time. We also examine an interesting simple example of this class of rules, one with an additive conserved "energy".