Monthly Archives: September 2012

Quasiperiodic pattern from eight waves and the Ammann-Beenker tiling

Using four waves at right angles we get a periodic structure of fourfold symmetry. A square grid of the same periodicity is easily fitted to this structure. Now, together with an extra set of four waves rotated by 45 degrees … Continue reading

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Patterns of waves with eight- and twelve-fold rotational symmetry

As discussed in the previous post “Quasiperiodic designs from superposition of waves” we get a quasiperiodic structure with eight-fold rotational symmetry using eight waves (n=8). Surprisingly, cosine waves of the same sign or alternating signs give us essentially the same … Continue reading

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Quasiperiodic designs from superposition of waves

Quasiperiodic crystals have sharp diffraction patterns with a quasiperiodic structure. Thus their atomic density is made of a corresponding set of sinusoidal waves. Inspired by these ideas I mixed waves to get quasiperiodic designs. Now, if you want to have … Continue reading

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Quasiperiodic designs and moiré patterns

Superimposing two square grids which are rotated by a small angle we get a strong moiré pattern, see a very interesting Wikipedia article. This pattern is roughly periodic. It weakens if the angle becomes very large. At an angle of … Continue reading

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Hiding the Ammann-Beenker tiling

I simply experimented around with changing angles of the dual lines. Then I had the idea to treat the two single grids differently. For the Ammann-Beenker tiling I got thus especially interesting results. For the square grid with horizontal and … Continue reading

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Twisting the tiling of dodecagons and triangles

In an earlier post (“Morphing the tiling of octagons and squares – a new twist“) I have varied the angles between the lines of the tiling and their generating grid lines. This gave us new tilings without mirror symmetry. I … Continue reading

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