The net created from the Penrose tiling is biLipschitz to the integer lattice
Metric Geometry
2007-11-26 v1 Dynamical Systems
Abstract
A separated net is a set of points which is relatively dense and uniformly discrete (another name for a Delone set). We are dealing with tilings and separated nets in Euclidean spaces and with the question whether a given separated net is biLipschitz to the integer lattice. In this paper we show, as an answer to a question of Burago and Kleiner, that the net that is obtained form the Penrose tiling is biLipschitz to the integer lattice.
Cite
@article{arxiv.0711.3707,
title = {The net created from the Penrose tiling is biLipschitz to the integer lattice},
author = {Y. Solomon},
journal= {arXiv preprint arXiv:0711.3707},
year = {2007}
}