Discrete Tomography of Mathematcal Quasicrystals: A Primer

This text is a report on work progress. We introduce the class of cyclotomic model sets (mathematical quasicrystals) Λ⊂Z[ξn], where Z[ξn] is the ring of integers in the nth cyclotomic field Q(ξn), and discuss the corresponding decomposition, consistency and reconstruction problems of the discrete tomography of these sets. Our solution of the so-called decomposition problem also applies to the case of the square lattice Z2=Z[ξ4], which corresponds to the classical setting of discrete tomography.