Topological properties of tiles

Benoit Loridant

Topological properties of tiles

Benoit Loridant

Chair of Mathematics, Statistics and Geometry (380)

Research output: Thesis › Doctoral Thesis

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Abstract

The topology of fractal tiles giving rise to a tessellation of the plane is investigated. This work leads to several criteria for a tile to be homeorphic to a closed disk. The criteria are all established by considering the neighbor configurations of the tiles in the tiling. A special class of tiles associated to canonical number systems is studied. The inner component of such a tile is described with the help of a finite graph.

Translated title of the contribution	Topologische Eigenschaften von Tiles
Original language	English
Qualification	Dr.mont.
Supervisors/Advisors	Thuswaldner, Jörg, Assessor A (internal) Drmota, Michael, Assessor B (external), External person
Publication status	Published - 2007

Bibliographical note

no embargo

Keywords

self-affine tiles
crystallographic tilings
canonical number systems

Access to Document

VolltextFinal published version, 59.3 MB

Cite this

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title = "Topological properties of tiles",

abstract = "The topology of fractal tiles giving rise to a tessellation of the plane is investigated. This work leads to several criteria for a tile to be homeorphic to a closed disk. The criteria are all established by considering the neighbor configurations of the tiles in the tiling. A special class of tiles associated to canonical number systems is studied. The inner component of such a tile is described with the help of a finite graph.",

keywords = "selbst-affine Pflaster, kristallographische Pflasterungen, kanonische Ziffernsysteme, self-affine tiles, crystallographic tilings, canonical number systems",

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T1 - Topological properties of tiles

AU - Loridant, Benoit

N1 - no embargo

PY - 2007

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N2 - The topology of fractal tiles giving rise to a tessellation of the plane is investigated. This work leads to several criteria for a tile to be homeorphic to a closed disk. The criteria are all established by considering the neighbor configurations of the tiles in the tiling. A special class of tiles associated to canonical number systems is studied. The inner component of such a tile is described with the help of a finite graph.

AB - The topology of fractal tiles giving rise to a tessellation of the plane is investigated. This work leads to several criteria for a tile to be homeorphic to a closed disk. The criteria are all established by considering the neighbor configurations of the tiles in the tiling. A special class of tiles associated to canonical number systems is studied. The inner component of such a tile is described with the help of a finite graph.

KW - selbst-affine Pflaster

KW - kristallographische Pflasterungen

KW - kanonische Ziffernsysteme

KW - self-affine tiles

KW - crystallographic tilings

KW - canonical number systems

M3 - Doctoral Thesis

ER -