Growth Forms of Tilings
Combinatorics
2025-08-28 v1 Discrete Mathematics
Abstract
The growth form (or corona limit) of a tiling is the limit form of its coordination shells, i.e. its set of tiles located at a fixed distance from some tile. We give an overview of current results, conjectures and open questions about growth forms, including periodic, multigrid, substitution, and hat tilings.
Keywords
Cite
@article{arxiv.2508.19928,
title = {Growth Forms of Tilings},
author = {Peter Hilgers and Anton Shutov},
journal= {arXiv preprint arXiv:2508.19928},
year = {2025}
}
Comments
Paper submitted to The Mathematical Intelligencer with one additional appendix