Combinatorial topology of three-dimensional self-affine tiles

Details Combinatorial topology of three-dimensional self-affine tiles Combinatorial topology of three-dimensional self-affine tiles

2010-02-03

arxiv.org/abs/1002.0710v1

Mathematics

Dynamical Systems

Scientific paper

We develop tools to study the topology and geometry of self-affine fractals in dimension three and higher. We use the self-affine structure and obtain rather detailed information about the connectedness of interior and boundary sets, and on the dimensions and intersections of boundary sets. As an application, we describe in algebraic terms the polyhedral structure of the six fractal three-dimensional twindragons. Only two of them can be homeomorphic to a ball but even these have faces which are not homeomorphic to a disk.

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