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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
 Fractal tiling of a sphere with octahedral twocolour symmetry
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Tag Archives: translational symmetry
Periodic design with 3fold rotational symmetry from 3dimensional space
Three dimensional space gives a threefold 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 spacediagonal from above, then you see an object with … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Tilings
Tagged kaleidoscope, Rotational symmetry, translational symmetry
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checkerboard coloring of quasiperiodic tilings
A long time ago I found a coloring of the rhombs of the AmmannBeenker tiling using two colors such that translations exchange colors, see “twofold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading
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 xcoordinate. Similarly, I take … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Selfsimilarity
Tagged anamorphosis, kaleidoscope, Selfsimilarity, translational symmetry
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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
Posted in Kaleidoscopes
Tagged kaleidoscope, Rotational symmetry, translational symmetry
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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
Posted in Kaleidoscopes
Tagged kaleidoscope, periodic design, Rotational symmetry, translational symmetry
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Wallpaper 2.0
Recently I bought an inexpensive secondhand 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
Posted in Extra
Tagged generative design, Quasiperiodic design, translational symmetry
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A special threecolor symmetry
Earlier I have presented a coloring of the AmmanBeenker 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
Posted in Tilings
Tagged Color, quasiperiodic Tiling, Selfsimilarity, translational symmetry
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