MULTIDIMENSIONAL STURMIAN SEQUENCES AND GENERALIZED SUBSTITUTIONS
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Publication:5483375
DOI10.1142/S0129054106004005zbMath1096.68125MaRDI QIDQ5483375
Publication date: 14 August 2006
Published in: International Journal of Foundations of Computer Science (Search for Journal in Brave)
multi-dimensional continued fractionssubstitutive sequencegeneralized substitutionBrun expansionmulti-dimensional Sturmian sequence
Related Items (17)
Functional stepped surfaces, flips, and generalized substitutions ⋮ Local rule substitutions and stepped surfaces ⋮ Circularly ordered dynamical systems ⋮ A study of Jacobi-Perron boundary words for the generation of discrete planes ⋮ Combinatorial generation of planar sets ⋮ Geometry, dynamics, and arithmetic of $S$-adic shifts ⋮ Approximation of digital surfaces by a hierarchical set of planar patches ⋮ Bracket words: A generalisation of Sturmian words arising from generalised polynomials ⋮ Brun expansions of stepped surfaces ⋮ Substitution discrete plane tilings with \(2n\)-fold rotational symmetry for odd \(n\) ⋮ About thin arithmetic discrete planes ⋮ S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry ⋮ Realization of aperiodic subshifts and uniform densities in groups ⋮ Geometrical models for a class of reducible Pisot substitutions ⋮ Discrete geometry and numeration ⋮ A combinatorial approach to products of Pisot substitutions ⋮ Arithmetic Discrete Planes Are Quasicrystals
Cites Work
- Two-dimensional iterated morphisms and discrete planes
- Periodicity and local complexity
- Substitutions in dynamics, arithmetics and combinatorics
- Combinatorics on patterns of a bidimensional Sturmian sequence
- Substitution invariant cutting sequences
- Towards a characterization of self-similar tilings in terms of derived Voronoï tessellations
- Tilings and rotations on the torus: A two-dimensional generalization of Sturmian sequences
- Geometric representation of substitutions of Pisot type
- A simple proof of the exponential convergence of the modified Jacobi–Perron algorithm
- Représentation géométrique de suites de complexité $2n+1$
- Dynamics of self-similar tilings
- Linearly recurrent subshifts have a finite number of non-periodic subshift factors
- On almost everywhere strong convergence of multi-dimensional continued fraction algorithms
- On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof
- Sequences with minimal block growth
- Symbolic Dynamics II. Sturmian Trajectories
- A characterization of Sturmian words by return words
- Double sequences of low complexity
- The rectangle complexity of functions on two-dimensional lattices
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