Self-affine fractals of finite type

• Autorzy: Christoph Bandt , Mathias Mesing
• Języki publikacji: EN

Abstrakty

EN

In the class of self-affine sets on ℝⁿ 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.

Kategorie tematyczne

• 51M20: Polyhedra and polytopes; regular figures, division of spaces
• 37F20: Combinatorics and topology
• 68Q70: Algebraic theory of languages and automata
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 84
• Numer: 1
• Strony: 131-148

Daty

wydano

2009

Twórcy

autor

Christoph Bandt

• Institute for Mathematics, Arndt University, 17487 Greifswald, Germany

autor

Mathias Mesing

• Institute for Mathematics, Arndt University, 17487 Greifswald, Germany

Identyfikatory

DOI

10.4064/bc84-0-9