Monthly Archives: April 2012

Why these tilings are not periodic

Often, you can put together two periodic patterns of different length and you get a new pattern, which is periodic too. The length of the period of the joint pattern is the least common multiple of the period lengths of … Continue reading

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Another variation on the Amman-Beenker tiling

Trying to get something new I used a grid of greater squares of length L=sqrt(2.) and a distance of 1 between their centers. This makes overlapping squares. Using two such grids as before (see “An easy way to quasiperiodic tilings“) … Continue reading

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Another tiling of eight-fold rotational symmetry

I am using the same basic method as for the Amman-Beenker tiling, see my post “How to find these corner points of the┬átiles“, but now with smaller squares. The distance between the centers of the squares remains equal to 1, … Continue reading

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Iteration of rhombs

We had good weather the last days and I enjoyed myself in the garden – weeding and admiring the nice tulips. I also found a nice iterative method to draw a tiling, which I will share with you now. It … Continue reading

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Twofold color symmetry in translation

I was a bit disappointed by results of the twofold color rotational symmetry shown in the previous post. Thus I was searching further and found something more interesting. In the earlier post “How to find these corner points of the … Continue reading

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Twofold color symmetry in rotation

Thinking of a checkerboard I wanted to do something similar with quasiperiodic tilings. The checkerboard is a square grid with two colors. A rotation by 90 degrees around a corner exchanges the colors, but else the board remains the same. … Continue reading

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The basic Amman-Beenker tiling

With the details presented in the earlier posts we can easily get large parts of this tiling. I have tried to choose colors, which are not too contrasting and too hard on the eyes: We see that small patterns are … Continue reading

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How to find these corner points of the tiles.

I am trying to explain all in detail and I hope that I will not be too boring. We first find the centers of the squares of the two square grids. If the length of their sides is equal to … Continue reading

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An easy way to quasiperiodic tilings

We want to make a tiling with 8-fold rotational symmetry. Thus we draw two square grids, one rotated by 45 degrees with respect to the other: If you turn this drawing by 45 degrees you get essentially the same image … Continue reading

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About tilings: Some basics

The most common tiling is the square grid: The whole plane is covered with squares. If you rotate it by 90 degrees (one-quarter turn) it looks the same. If you rotate it by 360 degrees (one turn) you see 4 … Continue reading

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