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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
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
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 tiles“, but now with smaller squares. The distance between the centers of the squares remains equal to 1, … Continue reading
Posted in Tilings
Tagged Art, Color, Math, Rotational symmetry, Tessellation, Tiling, translational symmetry
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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
Posted in Fractals, Tilings
Tagged Art, Color, fractal, iteration, processing, programming, Recreation, Tiling
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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
Posted in Tilings
Tagged Art, arts, Color, Pattern, quasiperiodic Tiling, Tessellation, translational symmetry
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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
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
Posted in Tilings
Tagged fractal, Geometry, Math, Quasiperiodicity, Recreation, Tessellation, Tile, Tiling
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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
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
Posted in Tilings
Tagged Art, Geometry, Math, quasiperiodic Tiling, Recreation, Tiling
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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
Posted in Tilings
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