TOPOLOGICAL STRUCTURE OF SELF-SIMILAR SETS

DOI10.1142/S0218348X0200104XzbMath1075.28005OpenAlexW2156857153MaRDI QIDQ5701549

Bo Tan, Jun Luo, Hui Rao

Publication date: 3 November 2005

Published in: Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218348x0200104x

zbMATH Keywords

self-similar setsimple closed curve

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Topological characterizations of particular spaces (54F65) Fractals (28A80)

Related Items (29)

On the fundamental group of self-affine plane tiles ⋮ The properties of a family of tiles with a parameter ⋮ A survey on topological properties of tiles related to number systems ⋮ Topological structure of a class of planar self-affine sets ⋮ Boundary local connectivity of tiles in \(\mathbb R^2\) ⋮ Topological properties of self-similar fractals with one parameter ⋮ Topological properties of a class of self-affine tiles in $\mathbb {R}^3$ ⋮ 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 ⋮ Self-affine manifolds ⋮ CONNECTEDNESS OF A CLASS OF SELF-AFFINE CARPETS ⋮ Topology of crystallographic tiles ⋮ A 1-dimensional Peano continuum which is not an IFS attractor ⋮ Connectedness of a class of planar self-affine tiles ⋮ Disk-like tiles and self-affine curves with noncollinear digits ⋮ Disk-like tiles derived from complex bases ⋮ Topology of connected self-similar tiles in the plane with disconnected interiors ⋮ Topology of planar self-affine tiles with collinear digit set ⋮ Fundamental group of tiles associated to quadratic canonical number systems ⋮ Fractal tiles and quasidisks ⋮ On cut sets of attractors of iterated function systems ⋮ Fractal squares with finitely many connected components ^* ⋮ Topological structure of fractal squares ⋮ Topological Properties of a Class of Higher-dimensional Self-affine Tiles ⋮ On the connected components of IFS fractals ⋮ A class of self-affine tiles in \(\mathbb{R}^d\) that are \(d\)-dimensional tame balls ⋮ Disklikeness of planar self-affine tiles ⋮ Every component of a fractal square is a Peano continuum ⋮ FRACTAL REP TILES OF ℝ2 AND ℝ3 USING INTEGER MATRICES

Cites Work

• Unnamed Item
• Integral self-affine tiles in \(\mathbb{R}^n\). II: Lattice tilings
• Haar bases for \(L^ 2 (\mathbb{R}^ n)\) and algebraic number theory
• Self-affine tiles in \(\mathbb{R}^n\)
• On the structure of self-similar sets
• Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/
• Classification of Self-Affine Lattice Tilings
• Remarks on Self-Affine Tilings
• Integral Self-Affine Tiles in ℝ ⁿ I. Standard and Nonstandard Digit Sets
• Self-similar lattice tilings

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