Tag Archives: Ammann–Beenker tiling

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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Hiding the Ammann-Beenker tiling

I simply experimented around with changing angles of the dual lines. Then I had the idea to treat the two single grids differently. For the Ammann-Beenker tiling I got thus especially interesting results. For the square grid with horizontal and … Continue reading

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Another tiling with octagons

I am addicted to iterative methods. They are easy to program and yield surprising results. I like to work out new iterative schemes, which have often their particular beauty. But the great suspense arises when running them first time on … Continue reading

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Blending tilings

Using semitransparent color to superpose tilings does not work out well because it is too difficult to control. Now I have a better idea. Simply draw the tilings as before. Then blend the pictures pixel by pixel by interpolating their … Continue reading

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Morphing the tiling of octagons and squares in space

An animated morphing of quasiperiodic tilings passes perhaps too rapidly. As tilings repeat throughout space it is quite natural to show their morphing depending on the position in  space or on the computer screen. This we can examine more easily. … Continue reading

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Morphing the Ammann-Beenker tiling

We can vary the dualization method in many ways. Here we play with the Ammann-Beenker tiling and use different lengths for the lines generated by the first square grid and the second square grid. This produces squares of different sizes … Continue reading

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Morphing the tiling of octagons and squares

In the last post “Doubling the tessellation of octagons and squares” I have used a grid of squares (in black) with diagonals (in blue). The blue lines are distinct and cannot be mapped onto the black lines by the symmetries … Continue reading

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Doubling the tessellation of octagons and squares

Regular octagons and squares make up a well-known semiregular tessellation that is often used to decorate floors Its dual grid is essentially a square grid with diagonal lines added. Four lines cross at the corner points giving the octagons of … Continue reading

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Iteration of rhombs: Filling the gap

In an earlier post “Iteration of rhombs” I got a fractal design of 8-fold rotational symmetry starting with a rhomb of acute angles of 45 degrees. An iterative step then replaces each rhomb by four rhombs, leaving a square gap … Continue reading

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