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.

27 pages, 9 figures

Cited by in corpus (10)

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• Magic numbers in the discrete tomography of cyclotomic model sets
• Discrete Tomography of Penrose Model Sets
• Discrete Tomography of Icosahedral Model Sets
• A Note on Affinely Regular Polygons
• Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets
• On the Existence of $U$-Polygons of Class $c\ge 4$ in Planar Point Sets
• Discrete Tomography of F-Type Icosahedral Model Sets
• Uniqueness in Discrete Tomography of Delone Sets with Long-Range Order
• Atomic Super-Resolution Tomography