The topological structure of fractal tilings generated by quadratic number systems

DOI10.1016/j.camwa.2004.09.008zbMath1123.11004OpenAlexW2040910565MaRDI QIDQ2387375

Shigeki Akiyama, Jörg M. Thuswaldner

Publication date: 2 September 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2004.09.008

zbMATH Keywords

AutomataFractalTilingConnectednessRadix representation

Mathematics Subject Classification ID

Related Items (22)

Dynamical directions in numeration ⋮ On the fundamental group of self-affine plane tiles ⋮ Bases of canonical number systems in quartic algebraic number fields ⋮ Boundary local connectivity of tiles in \(\mathbb R^2\) ⋮ Structure of planar integral self-affine tilings ⋮ A class of self-affine tiles in \(\mathbb{R}^3\) that are tame balls revisited ⋮ Boundary parametrization of planar self-affine tiles with collinear digit set ⋮ Interior components of a tile associated to a quadratic canonical number system ⋮ Self-affine manifolds ⋮ Representations for complex numbers with integer digits ⋮ Topology of crystallographic tiles ⋮ Boundary parametrization of self-affine tiles ⋮ Topology of a class of \(p2\)-crystallographic replication tiles ⋮ Crystallographic number systems ⋮ Topology of planar self-affine tiles with collinear digit set ⋮ INTERIOR COMPONENTS OF A TILE ASSOCIATED TO A QUADRATIC CANONICAL NUMBER SYSTEM — PART II ⋮ On a theorem of Bandt and Wang and its extension to \(p2\)-tiles ⋮ Number systems and tilings over Laurent series ⋮ A TECHNIQUE IN THE TOPOLOGY OF CONNECTED SELF-SIMILAR TILES ⋮ A class of self-affine tiles in \(\mathbb{R}^d\) that are \(d\)-dimensional tame balls ⋮ Disklikeness of planar self-affine tiles ⋮ FRACTAL REP TILES OF ℝ2 AND ℝ3 USING INTEGER MATRICES

Cites Work

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• Substitutions in dynamics, arithmetics and combinatorics
• Radix representations of quadratic fields
• Fractal geometry derived from complex bases
• On the boundary of self-affine tilings generated by Pisot numbers
• Self-affine tiles in \(\mathbb{R}^n\)
• Nombres algébriques et substitutions
• On the structure of self-similar sets
• Canonical number systems in imaginary quadratic fields
• Self-Similar Sets 5. Integer Matrices and Fractal Tilings of ℝ n
• Arithmetic construction of sofic partitions of hyperbolic toral automorphisms
• Dynamics of self-similar tilings
• The Hausdorff Dimension of the Boundary of a Self-Similar Tile
• Canonical number systems, counting automata and fractals
• Canonical number systems in algebraic number fields
• On periodic \(\beta\)-expansions of Pisot numbers and Rauzy fractals
• Topological properties of two-dimensional number systems
• Fractal properties of number systems
• Self-similar lattice tilings
• Pisot substitutions and Rauzy fractals
• Disk-like self-affine tiles in \(\mathbb{R}^2\)

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