Resumen de Canonical self-affine tilings by iterated function systems
Erin P. J. Pearse
An iterated function system Ø consisting of contractive affine mappings has a unique attractor F Rd which is invariant under the action of the system, as was shown by Hutchinson [3]. This paper shows how the action of the function system naturally produces a tiling T of the convex hull of the attractor. These tiles form a collection of sets whose geometry is typically much simpler than that of F, yet retains key information about both F and Ø. In particular, the tiles encode all the scaling data of Ø. We give the construction, along with some examples and applications. The tiling T is the foundation for the higher-dimensional extension of the theory of complex dimensions which was developed in [13] for the case d . 1.
