Designing aperiodic to periodic interfaces
Abstract
Symmetry sharing facilitates coherent interfaces which can transition from periodic to aperiodic structures. Motivated by the design and construction of such systems, we present hexagonal aperiodic tilings with a single edge-length which can be considered as decorations of a periodic lattice. We introduce these tilings by modifying an existing family of golden-mean trigonal and hexagonal tilings, and discuss their properties in terms of this wider family. Then, we show how the vertices of these new systems can be considered as decorations or sublattice sets of a periodic triangular lattice, before introducing methods to designing coherent aperiodic to periodic interfaces.
Cite
@article{arxiv.2404.11378,
title = {Designing aperiodic to periodic interfaces},
author = {Sam Coates},
journal= {arXiv preprint arXiv:2404.11378},
year = {2025}
}
Comments
Updated for clarity on motivation, and for inclusion of the aperiodic analogue to the dice or rhombille tiling. 11 (+4) pages, 6 (+4) figures