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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Category Archives: Tilings
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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Rotations, mirrorsymmetry and the scalar product
In the last post we have seen that scalar products between a pixel’s position in the output image and certain vectors e define periodic and quasiperiodic designs. We want symmetric images and thus we have to see how the scalar product changes … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming, Tilings
Tagged Math, mirror symmetry, Rotational symmetry
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Quasiperiodic and periodic kaleidoscopes from higher dimensional space
To get quasiperiodic and periodic designs in the twodimensional plane we first make a periodic decoration of higher dimensional space. Then we cut an infinitely thin twodimensional slice out of this space. This gives a design with rotational symmetry if … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design, Tilings
Tagged kaleidoscope, symmetry
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Trying to understand “Creating Symmetry”
I am struggling with the book: “Creating Symmetry – The Artful Mathematics of Wallpaper Patterns” by Frank A Farris, which I presented in my last post. As a very pedestrian mathematician and programmer I have difficulties with his abstract methods, based on complex … Continue reading
Posted in Kaleidoscopes, programming, Tilings
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Creating Symmetry
Recently I found a very exciting book: “Creating Symmetry – The Artful Mathematics of Wallpaper Patterns” by Frank A Farris. It has many beautiful images and explains the mathematics behind them very well, such that you could do your own work. His … Continue reading
Posted in Kaleidoscopes, Tilings
Tagged Art, generative design, Geometry, kaleidoscope, symmetry
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checkerboard coloring of tiling with 12fold rotational symmetry
At the risk of boring you I am showing the results of the checkerboard coloring as discussed in the last post, but now for 12fold rotational symmetry. Again the stars of rhombs have only one color: All squares have the … Continue reading
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