A TECHNIQUE IN THE TOPOLOGY OF CONNECTED SELF-SIMILAR TILES

DOI10.1142/S0218348X04002653zbMath1304.28009MaRDI QIDQ5497001

Tai-Man Tang, Sze-Man Ngai

Publication date: 30 January 2015

Published in: Fractals (Search for Journal in Brave)

zbMATH Keywords

iterated function systemtilingfractalcanonical number systemself-similar tileEisenstein set

Mathematics Subject Classification ID

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

Related Items (18)

On the fundamental group of self-affine plane tiles ⋮ A survey on topological properties of tiles related to number systems ⋮ Topological properties of self-similar fractals with one parameter ⋮ On self-affine tiles that are homeomorphic to a ball ⋮ SOME TOPOLOGICAL RESULTS ON LEVEL SETS AND MULTIFRACTAL SETS ⋮ Interior components of a tile associated to a quadratic canonical number system ⋮ Topology of crystallographic tiles ⋮ Disk-like tiles and self-affine curves with noncollinear digits ⋮ Boundary parametrization of self-affine tiles ⋮ Topology of connected self-similar tiles in the plane with disconnected interiors ⋮ Topology of planar self-affine tiles with collinear digit set ⋮ INTERIOR COMPONENTS OF A TILE ASSOCIATED TO A QUADRATIC CANONICAL NUMBER SYSTEM — PART II ⋮ CONNECTEDNESS OF SELF-AFFINE SETS WITH PRODUCT DIGIT SETS ⋮ On cut sets of attractors of iterated function systems ⋮ Topological structure of fractal squares ⋮ Disklikeness of planar self-affine tiles ⋮ Every component of a fractal square is a Peano continuum ⋮ BOUNDARY PARAMETRIZATION AND THE TOPOLOGY OF TILES

Cites Work

• Unnamed Item
• Unsolved problems in geometry
• The topological structure of fractal tilings generated by quadratic number systems
• A survey on topological properties of tiles related to number systems

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