Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets

DOI10.1016/j.jmaa.2012.05.034zbMath1285.52009arXiv1205.3552OpenAlexW2043737444MaRDI QIDQ441969

King-Shun Leung, Jun Jason Luo

Publication date: 8 August 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.3552

zbMATH Keywords

connectednessself-affine setcollinear digit setneighbor

Mathematics Subject Classification ID

Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (16)

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 ⋮ A criterion for self-similar sets to be totally disconnected ⋮ The connectedness of some two-dimensional self-affine sets ⋮ Topological properties of a class of self-affine tiles in $\mathbb {R}^3$ ⋮ CONNECTEDNESS OF A CLASS OF SELF-AFFINE CARPETS ⋮ Radix expansions and connectedness of planar self-affine fractals ⋮ Topology of a class of \(p2\)-crystallographic replication tiles ⋮ On the connectedness of planar self-affine sets ⋮ CONNECTEDNESS OF SELF-AFFINE SETS WITH PRODUCT DIGIT SETS ⋮ Topological structure of fractal squares ⋮ Topological Properties of a Class of Higher-dimensional Self-affine Tiles ⋮ Developments in fractal geometry ⋮ 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

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• Connectedness of a class of planar self-affine tiles
• Height reducing property of polynomials and self-affine tiles
• Height reducing problem on algebraic integers
• Expanding polynomials and connectedness of self-affine tiles
• Self-affine tiles in \(\mathbb{R}^n\)
• Disklikeness of planar self-affine tiles
• Disk-like tiles and self-affine curves with noncollinear digits
• Classification of Self-Affine Lattice Tilings
• On the Connectedness of Self-Affine Tiles
• Remarks on Self-Affine Tilings
• Self-similar lattice tilings
• Disk-like self-affine tiles in \(\mathbb{R}^2\)

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