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Monthly Archives: September 2012
Quasiperiodic pattern from eight waves and the AmmannBeenker 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
Patterns of waves with eight and twelvefold rotational symmetry
As discussed in the previous post “Quasiperiodic designs from superposition of waves” we get a quasiperiodic structure with eightfold rotational symmetry using eight waves (n=8). Surprisingly, cosine waves of the same sign or alternating signs give us essentially the same … Continue reading
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
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
Hiding the AmmannBeenker 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 AmmannBeenker tiling I got thus especially interesting results. For the square grid with horizontal and … Continue reading
Posted in Tilings
Tagged Ammann–Beenker tiling, morphing, quasiperiodic Tiling, Selfsimilarity
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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
Posted in Tilings
Tagged dual tesselation, enantiomorphic, mirror symmetry, quasiperiodic Tiling, Rotational symmetry
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