Abstract

In this paper we study properties of the fundamental domain F fi of number systems, which are defined in rings of integers of number fields. First we construct addition automata for these number systems. Since F fi defines a tiling of the n-dimensional vector space, we ask, which tiles of this tiling "touch" F fi . It turns out, that the set of these tiles can be described with help of an automaton, which can be constructed via an easy algorithm which starts with the above mentioned addition automaton. The addition automaton is also useful in order to determine the box counting dimension of the boundary of F fi . Since this boundary is a so-called graph-directed self affine set, it is not possible to apply the general theory for the calculation of the box counting dimension of self similar sets. Thus we have to use direct methods.

Citations