Local rules and global order, or aperiodic tilings

DOI10.1007/BF02984815zbMath1066.52501OpenAlexW2005917891MaRDI QIDQ1777517

Bruno Durand, Alexander Shen, Leonid A. Levin

Publication date: 23 May 2005

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

Full work available at URL: https://doi.org/10.1007/bf02984815

Mathematics Subject Classification ID

Combinatorics in computer science (68R05) Combinatorial aspects of tessellation and tiling problems (05B45) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

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A family of non-periodic tilings of the plane by right golden triangles ⋮ Coverability and multi-scale coverability on infinite pictures ⋮ Two-by-Two Substitution Systems and the Undecidability of the Domino Problem ⋮ Deterministic coloring of a family of complexes ⋮ Fixed-point tile sets and their applications ⋮ Fixed Point and Aperiodic Tilings ⋮ The Undecidability of the Domino Problem ⋮ An aperiodic set of 11 Wang tiles ⋮ Effective Closed Subshifts in 1D Can Be Implemented in 2D ⋮ Tilings: simulation and universality

Cites Work

• A small aperiodic set of Wang tiles
• Undecidability and nonperiodicity for tilings of the plane
• The undecidability of the domino problem
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