This Demonstration shows the sum of rotated plane waves animated by a phase parameter , where the density at a point is given by
For certain values of , you will observe a repeating crystalline pattern, which according to the crystallographic restriction theorem will be limited to 2-fold, 3-fold, 4-fold, or 6-fold rotational symmetry. Quasicrystals are very similar to crystals in that they have a highly ordered structure and rotational symmetry, but do not have the same restriction on the order of rotational symmetry. The crucial difference is that quasicrystals have no translational symmetry, so the patterns never repeat themselves.


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