Self-affine fractals of finite type

Tom 84 / 2009

Christoph Bandt, Mathias Mesing Banach Center Publications 84 (2009), 131-148 MSC: Primary 28A80; Secondary 51M20, 37F20, 68Q70. DOI: 10.4064/bc84-0-9

Streszczenie

In the class of self-affine sets on $\mathbb R^n$ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which decides whether the tile is homeomorphic to a disk.

Autorzy

  • Christoph BandtInstitute for Mathematics
    Arndt University
    17487 Greifswald, Germany
    e-mail
  • Mathias MesingInstitute for Mathematics
    Arndt University
    17487 Greifswald, Germany
    e-mail

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