It is proved that every pseudo-self-affine tiling in R is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronöı tessellations is a corollary. Previously, these results were obtained in the planar case, jointly with Priebe Frank. The new approach is based on the theory of graph-directed iterated function systems and su...

The self-similarity of polynomial curves is known to many. This paper builds on this idea by showing that polynomial curves called Bézier curves can be created and completely characterized by their self-affineness. A set of affine maps called an iterated function system can create self-affine sets. In this paper we prove that all Bézier curves can be created by iterated function systems.

For a self{similar or self{aane tile in R n we study the following questions: 1) What is the boundary? 2) What is the convex hull? We show that the boundary is a graph directed self{aane fractal, and in the self{similar case we give an algorithm to compute its dimension. We give necessary and suucient conditions for the convex hull to be a polytope, and we give a description of the Gauss map of...

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.