Forcing nonperiodicity with a single tile

DOI10.1007/s00283-011-9255-yzbMath1244.52014arXiv1009.1419OpenAlexW2964105946WikidataQ28109446 ScholiaQ28109446MaRDI QIDQ2429455

Joshua E. S. Socolar, Joan M. Taylor

Publication date: 27 April 2012

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1419

Mathematics Subject Classification ID

Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items

John Conway, tilings, and me ⋮ AN APERIODIC TILE WITH EDGE-TO-EDGE ORIENTATIONAL MATCHING RULES ⋮ Non-lattice-periodic tilings of \(\mathbb R^3\) by single polycubes ⋮ An aperiodic monotile that forces nonperiodicity through dendrites ⋮ The computation of overlap coincidence in Taylor-Socolar substitution tiling ⋮ A note on aperiodic Ammann tiles ⋮ Heesch Numbers of Edge-Marked Polyforms ⋮ Cayley graphs with an infinite Heesch number

Cites Work

• An aperiodic hexagonal tile
• The hexagonal parquet tiling: \(k\)-isohedral monotiles with arbitrarily large \(k\).
• Matching rules and substitution tilings
• Folds! II: Symmetry disturbed
• Penrose tilings as coverings of congruent decagons
• Heesch's Tiling Problem
• The undecidability of the domino problem
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