Quasiperiodic Patterns

Phys. Rev. Lett. 54, 2688 – Published 24 June 1985
Michel Duneau and André Katz


We present here a general framework to produce quasiperiodic tilings and more general quasiperiodic patterns in n dimensions corresponding to a finite number of local neighborings around each point. In particular, we give simple descriptions of the Penrose tilings of the plane and of a tiling of the three-dimensional space which exhibits an icosahedral symmetry. The Fourier transform of this last pattern is derived and shows a striking similarity with the electron-diffraction images obtained for a recently discovered alloy of Al and Mn.

DOI: http://dx.doi.org/10.1103/PhysRevLett.54.2688

  • Received 18 March 1985
  • Published in the issue dated 24 June 1985

© 1985 The American Physical Society

Authors & Affiliations

Michel Duneau and André Katz

  • Centre de Physique Théorique, Ecole Polytechnique, F-91128 Palaiseau Cedex, France

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