Matching Rules for the Sphinx Tiling Substitution

TL;DR

This paper presents a specific set of tiles that enforce the sphinx tiling substitution, demonstrating an aperiodic tiling system through matching rules.

Contribution

It introduces a tile set that enforces sphinx tiling substitution rules, establishing aperiodicity.

Findings

Tiles enforce sphinx tiling substitution

Tiles are proven to be aperiodic

Provides a constructive tile set for sphinx tiling

Abstract

We give a set of tiles that enforces the sphinx tiling substitution system; the tiles are thus aperiodic.