Projected Wallpaper Patterns

  • Isabel S. Labouriau
  • Eliana M. Pinho
Conference paper
Part of the Trends in Mathematics book series (TM)


Consider a periodic function f of two variables with symmetry Γ and let ⊂ Γ be the subgroup of translations. The Fourier expansion of a periodic function is a sum over *, the dual of the set of all the periods of f. After projecting f, some of its original symmetry remains. We describe the symmetries of the projected function, starting from Γ and from the structure of *.


Tilings in two dimensions crystallographic groups periodic solutions group-invariant bifurcations 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Isabel S. Labouriau
    • 1
  • Eliana M. Pinho
    • 2
  1. 1.Centro de Matemática da Universidade do PortoPortoPortugal
  2. 2.Departamento de Matemática AplicadaFaculdade de Ciências da Universidade do PortoPortoPortugal

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