Discrete Tomography of Planar Model Sets

Abstract

Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical quasicrystals. To this end, the class of cyclotomic model sets is introduced, and the corresponding consistency, reconstruction and uniqueness problems of the discrete tomography of these sets are discussed.