Tag Archives: translational symmetry

Periodic design with 3-fold rotational symmetry from 3-dimensional space

Three dimensional space gives a three-fold rotational symmetry in the drawing plane. The designs are periodic. Note that if you put a cube on one of its points and look along its space-diagonal from above, then you see an object with … Continue reading

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checkerboard coloring of quasiperiodic tilings

A long time ago I found a coloring of the rhombs of the Ammann-Beenker tiling using two colors such that translations exchange colors, see “two-fold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading

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repeated plane mapping, anamorphosis and mirrors

The image of the last post is quite bewildering. To get a calmer and simpler image I imposed mirror symmetries on the original image. A vertical mirror line results from taking the absolute value of the x-coordinate. Similarly, I take … Continue reading

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kaleidoscopic images with local rotational symmetry

The typical kaleidoscope has three mirrors in the shape of a triangular prism. One angle between the mirrors is 90 degrees. If the smallest angle between the mirrors is equal to 360 degrees divided by an even number, then we … Continue reading

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Periodic images from the kaleidoscope

It is still cold outside and the soil is frozen. Thus I have not much to do in the garden and a lot of time for this blog. In the previous article “How to program an ideal kaleidoscope” I have … Continue reading

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Wallpaper 2.0

Recently I bought an inexpensive second-hand copy of “The armchair universe – an exploration of computer worlds” by A. K. Dewdney. Printed in 1988 it is a real classic. Computers now have much more colors, pixels and memory and they … 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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