WOLFRAM|DEMONSTRATIONS PROJECT

Quasicrystals

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phase
color
SunsetColors
quality
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planes (n)
1
2
3
4
5
6
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8
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Instructions
• Click anywhere in the image to move to that point.
This Demonstration shows the sum of
n
rotated plane waves animated by a phase parameter
p
, where the density at a point
(x,y)
is given by
δ(x,y)
n
∑
k=1
cosxcos
πk
n
-ysin
πk
n
+p
.
For certain values of
n
, 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.