Cut-and-project quasicrystals, lattices, and dense forests release_iwmsxjelpraapf2xrsci5ghhye

by Faustin Adiceam, Yaar Solomon, Barak Weiss

Released as a article .

2019  

Abstract

Dense forests are discrete subsets of Euclidean space which are uniformly close to all sufficiently long line segments. The degree of density of a dense forest is measured by its visibility function. We show that cut-and-project quasicrystals are never dense forests, but their finite unions could be uniformly discrete dense forests. On the other hand, we show that finite unions of lattices typically are dense forests, and give a bound on their visibility function, which is close to optimal. We also construct an explicit finite union of lattices which is a uniformly discrete dense forest with an explicit bound on its visibility.
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Type  article
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Date   2019-07-08
Version   v1
Language   en ?
arXiv  1907.03501v1
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