Brimkov, Valentin2008-08-212008-08-212002Communication and Information Technology Research Technical Report 120, (2002)1178-3625http://hdl.handle.net/2292/2845You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s).In the present notes we define and study the notion of digital flatness. We extend to two dimensions various definitions and results about digital straightness, in particular, we resolve a conjecture of M. Nivat for the case of digital planes and define and characterize 2D Sturmian rays.Copyright CITR, The University of Auckland. You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site under terms that include this permission. All other rights are reserved by the author(s).https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmTechnical ReportFields of Research::280000 Information, Computing and Communication Sciences