MONTANUNIVERSITÄT LEOBEN INSTITUT FÜR MATHEMATIK UND ANGEWANDTE GEOMETRIE, ABTEILUNG FÜR MATHEMATIK UND STATISTIK FRANZ-JOSEF-STRAßE 18 A-8700 LEOBEN AUSTRIA FRANZ-JOSEF-STRAßE 18 A-8700 LEOBEN AUSTRIA
In this paper we compute the box counting dimension of sets, that are related to number systems in real quadratic number fields.
The sets under discussion are so-called graph-directed self affine sets. Contrary to the case of self similar sets, for self
affine sets there does not exist a general theory for the determination of the box counting dimension. Thus we are forced
to construct the covers, needed for its calculation, directly.