Communications in Mathematical Physics

, Volume 150, Issue 1, pp 23–44 | Cite as

Local rules for quasiperiodic tilings of quadratic 2-planes inR4

  • Le Thang Tu Quoc 
  • Sergey Piunikhin
  • Vladimir Sadov
Article

Abstract

We prove that quasiperiodic tilings of the plane, appearing in the strip projection method always admit local rules, when the linear embedding ofR2 inR4 has quadratic coefficients. These local rules are constructed and studied. The connection between Novikov quasicrystallographic groups and the quasiperiodic tilings of Euclidean space is explained. All the point groups in Novikov's sense, compatible with these local rules, are enlisted. The two-dimensional quasicrystals with infinite-fold rotational symmetry are constructed and studied.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Euclidean Space 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Le Thang Tu Quoc 
    • 1
  • Sergey Piunikhin
    • 1
  • Vladimir Sadov
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.ITP LandauMoscowRussia

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