Monthly Archives: July 2012

Another tiling of dodecagonal symmetry

We consider self-similarities and iteration methods for quasiperiodic tilings of 12-fold symmetry. In “Iteration of rhombs: filling the gap (2)” the ratio of the lengths at each iteration step is sqrt(2+sqrt(3))=sqrt(3.73)=1.91. The Stampfli tiling has a self-similarity (see “Exhibition of … 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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A special three-color symmetry

Earlier I have presented a coloring of the Amman-Beenker tiling which exchanges colors upon translation, see “Twofold color symmetry in translation” and “Twofold color symmetry in translation – revisited“. It resulted from the square checkerboard. As there are many similarities … Continue reading

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Three-color symmetry in rotation for the Stampfli tiling

I am going back to color symmetries of the Stampfli tiling. In an earlier post I showed a two-color symmetry in rotation. Now I am discussing a symmetry with three colors. A rotation of the tiling by 30 degrees should … Continue reading

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Variations on a star

I still have a lot to do on tilings of 12-fold rotational symmetry – but summer is too hot to do serious work. Meanwhile I amuse myself with iterative decorations. Two triangles superimposed form a six-pointed star. This is a … Continue reading

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Another enantiomorphic tiling

In the last post “doubling the tessellation of squares and triangles” I have shown a quasiperiodic tiling with an unusual mirror symmetry. Earlier in “Morphing the tiling … a new twist” I got a tiling which is not at all … Continue reading

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Doubling the tessellation of squares and triangles

Equilateral triangles do not fit well with four-fold rotational symmetry. Yet there exists a semiregular tessellation having both. It has unusual symmetries. The centers of the rotational symmetries are at the center of the squares. It is mirror symmetric but … Continue reading

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