Digital Flatness

  • Valentin E. Brimkov
  • Reneta P. Barneva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


In this paper we define and study the notion of digital flatness. We extend to dimension two various definitions and classical results about digital lines and rays. In particular, we resolve a conjecture of Maurice Nivat restricted to the case of digital planes, and define and characterize 2D Sturmian rays.


Digital planarity 2D Sturmian word periodic array digitization of planes slope of digital planes 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Valentin E. Brimkov
    • 1
  • Reneta P. Barneva
    • 2
  1. 1.Inst. of Math. and Comp. ScienceBulg. Acad. of Sci.SofiaBulgaria
  2. 2.SUNY FredoniaFredoniaUSA

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