Tag Archives: Quasiperiodicity

Projection method for 10-fold rotational symmetry

We reconsider the projection method for the Ammann-Beenker 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

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Periodic approximations of quasiperiodic tilings

In the earlier post “Why these tilings are not periodic” I showed that the Ammann-Beenker 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

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Another rotation from four- to eight-fold rotational symmetry

There are different possibilities to orient a four-dimensional periodic pattern around the two-dimensional drawing plane such that we see a periodic pattern of four-fold rotational symmetry. In contrast to the last post we will now use a symmetric choice. The … Continue reading

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Periodic and quasiperiodic images from cross-sections of 4-dimensional space

In the earlier post “Quasiperiodic designs from waves and higher dimensional space” I have shown that the quasiperiodic wave pattern with 8-fold rotational symmetry is a special cross-section of a periodic pattern in  4-dimensional space. Here I will rotate the … Continue reading

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Design from waves with ten-fold rotational symmetry using another color model

Instead of controlling directly the color components red, green and blue with the waves we can use the hue-saturation-brightness color model. In this example the waves of lowest frequency change the brightness. Waves of higher frequency change the hue. Saturation … Continue reading

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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 Ammann-Beenker tiling using two square grids. Then in “How to find these corner points of … 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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