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Tag Archives: Ammann–Beenker tiling
Beautifying the double grid
The grids for quasiperiodic tilings do not look good because a lot of irregular shapes arise from superimposing two simple grids, see the article “Doubling the tessellation of triangles“. But we can distort these double grids and get new interesting … Continue reading
Posted in Tilings
Tagged Ammann–Beenker tiling, dual tesselation, Geometry, islamic art, quasiperiodic Tiling, Stampfli tiling
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Periodic approximations of quasiperiodic tilings
In the earlier post “Why these tilings are not periodic” I showed that the AmmannBeenker tiling is quasiperiodic because it arises from superimposing two square grids with rotated by 45 degrees. As seen in the same direction we have the periodic … Continue reading
Posted in Tilings
Tagged Ammann–Beenker tiling, dual tesselation, quasiperiodic Tiling, Quasiperiodicity
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Stampflitiling and related designs from waves
Three sinusoidal waves make a hexagonal pattern for f(x,y)=cos(x)+cos(x/2+sqrt(3) y/2)+ cos(x/2+sqrt(3) y/2), see the figure at left. Using this and the same pattern rotated by 90 degrees we get patterns of 12fold rotational symmetry. I found it interesting to draw … Continue reading
Periodic and quasiperiodic images from crosssections of 4dimensional space
In the earlier post “Quasiperiodic designs from waves and higher dimensional space” I have shown that the quasiperiodic wave pattern with 8fold rotational symmetry is a special crosssection of a periodic pattern in 4dimensional space. Here I will rotate the … Continue reading
Quasiperiodic designs from waves and higher dimensional space
I am doing it again – a rather mathematical post. Well, in “An easy way to quasiperiodic tilings” I have shown how to make the AmmannBeenker tiling using two square grids. Then in “How to find these corner points of … Continue reading
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