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Tag Archives: Ammann–Beenker tiling
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
Hiding the AmmannBeenker 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 AmmannBeenker tiling I got thus especially interesting results. For the square grid with horizontal and … Continue reading
Posted in Tilings
Tagged Ammann–Beenker tiling, morphing, quasiperiodic Tiling, Selfsimilarity
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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
Posted in Tilings
Tagged Ammann–Beenker tiling, Iterative method, quasiperiodic Tiling, Rotational symmetry
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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
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
Posted in Tilings
Tagged Ammann–Beenker tiling, animation, Art, Geometry, morphing, quasiperiodic Tiling
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Morphing the AmmannBeenker tiling
We can vary the dualization method in many ways. Here we play with the AmmannBeenker 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
Posted in Fractals
Tagged Ammann–Beenker tiling, animation, Art, Geometry, morphing, quasiperiodic Tiling
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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
Posted in Tilings
Tagged Ammann–Beenker tiling, Art, quasiperiodic Tiling, Rotational symmetry, Tessellation
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Doubling the tessellation of octagons and squares
Regular octagons and squares make up a wellknown 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
Posted in Tilings
Tagged Ammann–Beenker tiling, Art, Geometry, quasiperiodic Tiling, Rotational symmetry, Tessellation
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Iteration of rhombs: Filling the gap
In an earlier post “Iteration of rhombs” I got a fractal design of 8fold 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
Posted in Tilings
Tagged Ammann–Beenker tiling, Art, fractal, Iterative method, quasiperiodic Tiling, Rotational symmetry, Selfsimilarity
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