PSEUDO-SELF-AFFINE TILINGS IN Rd

Self-Affine Tiles in Rn

A self-affine tile in R is a set T of positive measure with A(T) = d ∈ $ < (T + d), where A is an expanding n × n real matrix with det (A) = m on integer, and $ = {d 1 ,d 2 , . . . , d m } ⊆ R is a set of m digits. It is known that self-affine tiles always give tilings of R by translation. This paper extends the known characterization of digit sets $ yielding self-affine tiles. It proves seve...

Neighbours of Self–Affine Tiles in Lattice Tilings

Let T be a tile of a self-affine lattice tiling. We give an algorithm that allows to determine all neighbours of T in the tiling. This can be used to characterize the sets VL of points, where T meets L other tiles. Our algorithm generalizes an algorithm of the authors which was applicable only to a special class of self-affine lattice tilings. This new algorithm can also be applied to classes c...

Remarks on Self-Affine Tilings

We study self-affine tilings of R n with special emphasis on the two-digit case. We prove that in this case the tile is connected and, if n 3, is a lattice-tile.

On the Boundary of Self Affine Tilings Generated by Pisot Numbers

On the Characterization of Expansion Maps for Self-Affine Tilings

We consider self-affine tilings in R with expansion matrix φ and address the question which matrices φ can arise this way. In one dimension, λ is an expansion factor of a self-affine tiling if and only if |λ| is a Perron number, by a result of Lind. In two dimensions, when φ is a similarity, we can speak of a complex expansion factor, and there is an analogous necessary condition, due to Thurst...