All Outputs (2)

An aperiodic tile with edge-to-edge orientational matching rules (2021)
Journal Article
Walton, J. J., & Whittaker, M. F. (2021). An aperiodic tile with edge-to-edge orientational matching rules. Journal of the Institute of Mathematics of Jussieu, https://doi.org/10.1017/s1474748021000517

We present a single, connected tile which can tile the plane but only nonperiodically. The tile is hexagonal with edge markings, which impose simple rules as to how adjacent tiles are allowed to meet across edges. The first of these rules is a standa... Read More about An aperiodic tile with edge-to-edge orientational matching rules.

Aperiodicity, rotational tiling spaces and topological space groups (2021)
Journal Article
Hunton, J., & Walton, J. J. (2021). Aperiodicity, rotational tiling spaces and topological space groups. Advances in Mathematics, 388, Article 107855. https://doi.org/10.1016/j.aim.2021.107855

We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational structure... Read More about Aperiodicity, rotational tiling spaces and topological space groups.