An aperiodic hexagonal tile

DOI10.1016/j.jcta.2011.05.001zbMath1232.05052arXiv1003.4279OpenAlexW2043318682WikidataQ61311188 ScholiaQ61311188MaRDI QIDQ640835

Joshua E. S. Socolar, Joan M. Taylor

Publication date: 21 October 2011

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4279

zbMATH Keywords

tilingsubstitutionaperiodicmatching rules

Mathematics Subject Classification ID

Combinatorial aspects of tessellation and tiling problems (05B45)

Related Items (17)

Fractal tilings based on successive adjacent substitution rule ⋮ Hexagonal inflation tilings and planar monotiles ⋮ Taylor-Socolar hexagonal tilings as model sets ⋮ Resiliency to multiple nucleation in temperature-1 self-assembly ⋮ AN APERIODIC TILE WITH EDGE-TO-EDGE ORIENTATIONAL MATCHING RULES ⋮ Undecidable translational tilings with only two tiles, or one nonabelian tile ⋮ Forcing nonperiodicity with a single tile ⋮ Non-lattice-periodic tilings of \(\mathbb R^3\) by single polycubes ⋮ Aperiodic tilings with one prototile and low complexity atlas matching rules ⋮ An aperiodic monotile that forces nonperiodicity through dendrites ⋮ The computation of overlap coincidence in Taylor-Socolar substitution tiling ⋮ Uncovering multiscale order in the prime numbers via scattering ⋮ A note on aperiodic Ammann tiles ⋮ Rectangular tileability and complementary tileability are undecidable ⋮ Forcing nonperiodic tilings with one tile using a seed ⋮ Resiliency to Multiple Nucleation in Temperature-1 Self-Assembly ⋮ Cayley graphs with an infinite Heesch number

Uses Software

• OEIS

Cites Work

• The hexagonal parquet tiling: \(k\)-isohedral monotiles with arbitrarily large \(k\).
• Wire bending
• Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
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