Combinatorics on patterns of a bidimensional Sturmian sequence

DOI10.1016/S0304-3975(97)00117-5zbMath0913.68206OpenAlexW462256MaRDI QIDQ1274927

Laurent Vuillon

Publication date: 12 January 1999

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-3975(97)00117-5

zbMATH Keywords

discrete geometrycombinatorics on patternscomplexity and tilings of the plane

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (19)

Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions ⋮ On a conjecture on bidimensional words. ⋮ Generation and recognition of digital planes using multi-dimensional continued fractions ⋮ Hybrid quasicrystals, transport and localization in products of minimal sets ⋮ Digital planarity -- a review ⋮ Two-dimensional iterated morphisms and discrete planes ⋮ A characterization of Sturmian words by return words ⋮ Maximal pattern complexity of higher dimensional words ⋮ Double sequences of low complexity ⋮ Plane digitization and related combinatorial problems ⋮ Maximal pattern complexity of two-dimensional words ⋮ Strong cocycle triviality for \(Z^{2}\) subshifts ⋮ The rectangle complexity of functions on two-dimensional lattices ⋮ Generation and Recognition of Digital Planes Using Multi-dimensional Continued Fractions ⋮ About the Frequencies of Some Patterns in Digital Planes Application to Area Estimators ⋮ MULTIDIMENSIONAL STURMIAN SEQUENCES AND GENERALIZED SUBSTITUTIONS ⋮ Recurrence along directions in multidimensional words ⋮ The complexity of functions on lattices ⋮ Balance properties of multi-dimensional words

Cites Work

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• Updown generation of Penrose patterns
• On the number of factors of Sturmian words
• On Rauzy fractal
• On the complexity of infinite sequences
• Complexity of trajectories in rectangular billiards
• Représentation géométrique de suites de complexité $2n+1$
• Complexity of sequences defined by billiard in the cube
• Complexité de suites définies par des billards rationnels
• Sequences with minimal block growth

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