A Survey on Topological Properties of Tiles Related to Number Systems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2004-12

AUTHORS

Shigeki Akiyama, Jörg M. Thuswaldner

ABSTRACT

In the present paper we give an overview of topological properties of self-affine tiles. After reviewing some basic results on self-affine tiles and their boundary we give criteria for their local connectivity and connectivity. Furthermore, we study the connectivity of the interior of a family of tiles associated to quadratic number systems and give results on their fundamental group. If a self-affine tile tessellates the space the structure of the set of its ‘neighbors’ is discussed. More... »

PAGES

89-105

References to SciGraph publications

  • 1997-01. Integral self-affine tiles in ℝn part II: Lattice tilings in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 1981-03. Canonical number systems in imaginary quadratic fields in ACTA MATHEMATICA HUNGARICA
  • 2003. Neighbours of Self-affine Tiles in Lattice Tilings in FRACTALS IN GRAZ 2001
  • 2001-01-01. Disk-Like Self-Affine Tiles in R2 in DISCRETE & COMPUTATIONAL GEOMETRY
  • 1985-12. On the structure of self-similar sets in JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
  • 1994-05. Self-Similar Lattice Tilings in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 2003-05. The Heighway Dragon Revisited in DISCRETE & COMPUTATIONAL GEOMETRY
  • 1999-04. Self-Replicating Tiles and Their Boundary in DISCRETE & COMPUTATIONAL GEOMETRY
  • 1994-07. Crystallographic reptiles in GEOMETRIAE DEDICATA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10711-004-1774-7

    DOI

    http://dx.doi.org/10.1007/s10711-004-1774-7

    DIMENSIONS

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