Cut‐and‐project quasicrystals, lattices and dense forests

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