Generating Discrete Planes with Substitutions

  • Valérie Berthé
  • Jérémie Bourdon
  • Timo Jolivet
  • Anne Siegel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8079)


Given a finite set S of unimodular Pisot substitutions, we provide a method for characterizing the infinite sequences over S that allow to generate a full discrete plane when, starting from a finite seed, we iterate the multidimensional dual substitutions associated with S. We apply our results to study the substitutions associated with the Brun multidimensional continued fraction algorithm.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Valérie Berthé
    • 1
  • Jérémie Bourdon
    • 2
  • Timo Jolivet
    • 1
    • 3
  • Anne Siegel
    • 4
  1. 1.LIAFA, CNRSUniversité Paris DiderotFrance
  2. 2.LINAUniversité de NantesFrance
  3. 3.FUNDIM, Department of MathematicsUniversity of TurkuFinland
  4. 4.INRIA, Centre Rennes-Bretagne AtlantiqueDylissRennesFrance

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