Disklikeness of planar self-affine tiles

DOI10.1090/S0002-9947-07-04106-2zbMath1118.52023MaRDI QIDQ3431217

King-Shun Leung, Ka-Sing Lau

Publication date: 5 April 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

self-affine tileslattice tilingsdisklike tiles

Mathematics Subject Classification ID

Fractals (28A80) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (37)

Duality questions for operators, spectrum and measures ⋮ Topological structure of a class of planar self-affine sets ⋮ Boundaries of disk-like self-affine tiles ⋮ A characterization of connected self-affine fractals arising from collinear digits ⋮ Topological properties of self-similar fractals with one parameter ⋮ Rational self-affine tiles ⋮ A criterion for self-similar sets to be totally disconnected ⋮ Self-affine tiles generated by a finite number of matrices ⋮ Structure of planar integral self-affine tilings ⋮ Topological properties of a class of self-affine tiles in $\mathbb {R}^3$ ⋮ Boundary parametrization of planar self-affine tiles with collinear digit set ⋮ Connectedness of a class of two-dimensional self-affine tiles associated with triangular matrices ⋮ On self-affine tiles that are homeomorphic to a ball ⋮ Self-affine manifolds ⋮ Some Recent Developments of Self-Affine Tiles ⋮ Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets ⋮ CONNECTEDNESS OF A CLASS OF SELF-AFFINE CARPETS ⋮ Characterization of a class of planar self-affine tile digit sets ⋮ Ergodic scales in fractal measures ⋮ Connectedness of a class of planar self-affine tiles ⋮ Height reducing property of polynomials and self-affine tiles ⋮ Radix expansions and connectedness of planar self-affine fractals ⋮ Disk-like tiles and self-affine curves with noncollinear digits ⋮ Topology of a class of \(p2\)-crystallographic replication tiles ⋮ Topology of planar self-affine tiles with collinear digit set ⋮ On the connectedness of planar self-affine sets ⋮ Fractal tiles and quasidisks ⋮ On self-affine tiles whose boundary is a sphere ⋮ REMARKS ON SELF-AFFINE FRACTALS WITH POLYTOPE CONVEX HULLS ⋮ CONNECTEDNESS OF SELF-AFFINE SETS WITH PRODUCT DIGIT SETS ⋮ Classification of tile digit sets as product-forms ⋮ Spectral measures and Cuntz algebras ⋮ Topological structure of fractal squares ⋮ Topological Properties of a Class of Higher-dimensional Self-affine Tiles ⋮ Spectral structure of digit sets of self-similar tiles on ${\mathbb R}^1$ ⋮ A class of self-affine tiles in \(\mathbb{R}^d\) that are \(d\)-dimensional tame balls ⋮ Connectedness of planar self-affine sets associated with non-collinear digit sets

Cites Work

• Unnamed Item
• Unnamed Item
• Integral self-affine tiles in \(\mathbb{R}^n\). II: Lattice tilings
• Expanding polynomials and connectedness of self-affine tiles
• On the connectedness of self-affine attractors
• Self-affine tiles in \(\mathbb{R}^n\)
• The topological structure of fractal tilings generated by quadratic number systems
• A survey on topological properties of tiles related to number systems
• Arithmetic Properties of Bernoulli Convolutions
• On the structure of self-similar sets
• Complex Numbers with Three Radix Expansions
• Self-Similar Sets 5. Integer Matrices and Fractal Tilings of ℝ n
• Non-Negative Digit Sets in Positional Number Systems
• Classification of Self-Affine Lattice Tilings
• On the Connectedness of Self-Affine Tiles
• DISCLIKE LATTICE REPTILES INDUCED BY EXACT POLYOMINOES
• On the boundary connectedness of connected tiles
• Remarks on Self-Affine Tilings
• Integral Self-Affine Tiles in ℝ ⁿ I. Standard and Nonstandard Digit Sets
• A TECHNIQUE IN THE TOPOLOGY OF CONNECTED SELF-SIMILAR TILES
• TOPOLOGICAL STRUCTURE OF SELF-SIMILAR SETS
• Topological properties of two-dimensional number systems
• Disk-like self-affine tiles in \(\mathbb{R}^2\)

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