Tilings: recursivity and regularity

  • Authors:

  • Julien Cervelle;Bruno Durand

  • Affiliations:

  • LIF - CMI, Technopole de Chateau-Gombert, 39 rue Joliot-Curie, 13453 Marseille, Cedex 13, France;LIF - CMI, Technopole de Chateau-Gombert, 39 rue Joliot-Curie, 13453 Marseille, Cedex 13, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

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Abstract

We establish a first step towards a "Rice theorem" for tilings: for non-trivial sets, it is undecidable to know whether two different tile sets produce the same tilings of the plane. Then, we study quasiperiodicity functions associated with tilings. This function is a way to measure the regularity of tilings. We prove that, not only almost all recursive functions can be obtained as quasiperiodicity functions, but also, a function which overgrows any recursive function.