Magic numbers in the discrete tomography of cyclotomic model sets

Abstract

We report recent progress in the problem of distinguishing convex subsets of cyclotomic model sets $\Lambda$ by (discrete parallel) X-rays in prescribed $\Lambda$-directions. It turns out that for any of these model sets $\Lambda$ there exists a `magic number' $m_{\Lambda }$ such that any two convex subsets of $\Lambda$ can be distinguished by their X-rays in any set of $m_{\Lambda }$ prescribed $\Lambda$-directions. In particular, for pentagonal, octagonal, decagonal and dodecagonal model sets, the least possible numbers are in that very order 11, 9, 11 and 13.

6 pages, 1 figure; based on the results of arXiv:1101.4149 [math.MG]; presented at Aperiodic 2012 (Cairns, Australia)

References in corpus (2)

• Discrete Tomography of Planar Model Sets
• Discrete Tomography of Icosahedral Model Sets

Cited by in corpus (4)

• On a Family of Random Noble Means Substitutions
• On the Entropy of a Two Step Random Fibonacci Substitution
• A patchy-particle 3-dimensional octagonal quasicrystal
• Discrete tomography: Magic numbers for $N$-fold symmetry