Local generation of tilings

TL;DR

This paper explores methods for locally generating all configurations of a subshift, introducing new definitions, analyzing their properties, and providing techniques and examples to determine when a subshift can be locally generated.

Contribution

It introduces two new definitions of local generation for subshifts and develops techniques to verify these properties, advancing understanding of local configurational generation.

Findings

Proposed two definitions of local generation.

Developed techniques to verify local generation.

Illustrated results with multiple examples.

Abstract

In this article, we investigate the possibility of generating all the configurations of a subshift in a local way. We propose two definitions of local generation, explore their properties and develop techniques to determine whether a subshift satisfies these definitions. We illustrate the results with several examples.