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Tag Archives: Quasiperiodicity
Projection method for 10fold rotational symmetry
We reconsider the projection method for the AmmannBeenker tiling, see the post “An easy way to quasiperiodic tilings” and have a look at the square lattices. Each can be made with two sets of periodically spaced parallel lines at right … Continue reading
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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Another rotation from four to eightfold rotational symmetry
There are different possibilities to orient a fourdimensional periodic pattern around the twodimensional drawing plane such that we see a periodic pattern of fourfold rotational symmetry. In contrast to the last post we will now use a symmetric choice. The … 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
Design from waves with tenfold rotational symmetry using another color model
Instead of controlling directly the color components red, green and blue with the waves we can use the huesaturationbrightness color model. In this example the waves of lowest frequency change the brightness. Waves of higher frequency change the hue. Saturation … Continue reading
Posted in Quasiperiodic design
Tagged Color, Quasiperiodic design, Quasiperiodicity, Rotational symmetry
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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
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