In the last 30 years, the mathematical theory of aperiodic order has developed enormously.
Many new tilings and properties have been discovered, few of which are covered or …

This collaborative volume presents recent trends arising from the fruitful interaction between
the themes of combinatorics on words, automata and formal language theory, and number …

We are concerned with the tiling flow T associated to a substitution φ over a finite alphabet.
Our focus is on substitutions that are unimodular Pisot, ie, their matrix is unimodular and has …

Our goal is to present a unified and reasonably complete account of the various conjectures,
known as Pisot conjectures, that assert that certain dynamical systems arising from …

Tilings based on the cut-and-project method are key model systems for the description of
aperiodic solids. Typically, quantities of interest in crystallography involve averaging over …

This paper is intended to provide an introduction to the theory of substitution tilings. For our
purposes, tiling substitution rules are divided into two broad classes: geometric and …

We introduce a formalism for handling general spaces of hierarchical tilings, a category that
includes substitution tilings, Bratteli–Vershik systems, S-adic transformations, and multi …

We consider self-affine tilings in the Euclidean space and the associated tiling dynamical
systems, namely, the translation action on the orbit closure of the given tiling. We investigate …

We introduce two new characterizations of Meyer sets. A repetitive Delone set in ℝ d of finite
local complexity is topologically conjugate to a Meyer set if and only if it has d linearly …

We develop a systematic approach to continuous substitutions on compact Hausdorff
alphabets. Focussing on implications of irreducibility and primitivity, we highlight important …