What is Aperiodic Order

By Michael Baake, David Damanik, Uwe Grimm. 2002

380 citations recorded by the source corpus.

The theory of aperiodic order is concerned with the development of ideas stimulated by the discovery of quasicrystals. We give a gentle introduction to some mathematical aspects of aperiodic order, aimed at a more general audience.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/06167b29574e5c03bc0e0a9454d2a79c9212e120

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Materials Chemistry

Citations in the corpus

On the Pisot Substitution Conjecture (2015, methodology): “See also [16, Example 5.8] for a discussion of the Frank-Robinson tiling and see [94] for more examples of non-FLC ‘fusion’ tilings.”
On weak model sets of extremal density (2015, methodology): “As a consequence of the translation boundedness of ω, this sequence has at least one vague accumulation point, each of which is called an autocorrelation measure of ω; see [21] or [1] for background.”
Dynamics on the graph of the torus parametrization (2015, background): “We also mention the recent comprehensive monograph by Baake and Grimm [2].”
Approximate lattices (2016, background): “Invariant measures on right-hulls of subsets of Rn have received much attention in the context of the dynamical approach to tilings and mathematical quasi-crystals (see [32], and also [3] for a general overview and recent reference list of the subject).”