Canonical Number Systems , Counting Automata and Fractals

  title={Canonical Number Systems , Counting Automata and Fractals},
  author={Klaus Scheicher and J{\"o}rg M. Thuswaldner},
In this paper we study properties of the fundamental domain Fβ of number systems, which are defined in rings of integers of number fields. First we construct addition automata for these number systems. Since Fβ defines a tiling of the n-dimensional vector space, we ask, which tiles of this tiling “touch” Fβ . 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… CONTINUE READING