Aperiodic Tilings, Order, and Randomness

2023/08/10 by Rodrigo Treviño · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Mathematics · #Aperiodic graph #Cellular Automata and Applications #Combinatorics #Computer science #DNA and Biological Computing #Geometry #Mathematics #Order (exchange) #Physics #Quasicrystal #Quasicrystal Structures and Properties #Randomness #Statistical physics #Statistics #Substitution tiling

paper · pdf · doi:10.1090/noti2759

published in Notices of the American Mathematical Society 70(08), 1 (American Mathematical Society)

openalex publication_date 2023/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

The study of aperiodic tilings is at the crossroads of many branches of mathematics, and so there are many points of view and many tools available to study them. There are also many open questions, especially for tilings in higher dimensions.

Cited by

• Electron model on Truchet tiling: Extended-to-localized transitions and asymmetric spectrum
• Lattice tilings of Hilbert spaces

Related

• Conway and aperiodic tilings
• On the noncommutative geometry of tilings
• Tilings with infinite local complexity
• Aperiodic Tilings on the Computer
• An aperiodic tiling made of one tile, a triangle