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An Aperiodic Monotile for the Tiler by Van Dongen, Vincent is a scholarly article available to read on EtoBox.

What is An Aperiodic Monotile for the Tiler about?

Can the entire plane be paved with a single tile that forces aperiodicity? This is known as the ein Stein problem (in German, ein Stein means one tile). This paper presents an aperiodic monotile for the tiler. It is based on the monotile developed by Taylor and Socolar (whose aperiodicity is forced by means of a non-connected tile that is mainly hexagonal) and motif-based hexagonal tilings that followed this major discovery. The proposed monotile consists of two layers. No motif is needed to make the monotile aperiodic. Additional motifs can be added to the monotile to provide some insights. The proof of aperiodicity is presented with the use of such motifs.

Author

Van Dongen, Vincent

Published

2022

Language

EN