Projected Wallpaper Patterns
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Consider a periodic function f of two variables with symmetry Γ and let ℒ ⊂ Γ be the subgroup of translations. The Fourier expansion of a periodic function is a sum over ℒ*, the dual of the set ℒ 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 ℒ*.
KeywordsTilings in two dimensions crystallographic groups periodic solutions group-invariant bifurcations
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