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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: Quasiperiodic design
Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
Using the recipe of the last post for fourdimensional space (p=4) I got this image of 8fold rotational symmetry: A center of approximate 8fold rotational symmetry is near the lower left corner. Large brown patches appear at roughly equal distances. … Continue reading
Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
We now want to impose inversion symmetry in addition to rotational symmetry on our designs. This means that the mapping functions should not change upon inversion of the position. Thus X(x,y)=X(x,y) and Y(x,y)=Y(x,y). Let’s consider space with an odd number … Continue reading
quasiperiodic patterns of 5fold symmetry from 5 dimensional space
I now want to see some images. Using a photo of a caterpillar as input image I get I used the simplest quasiperiodic mapping functions resulting from the theory of the last post and The center of perfect 5fold symmetry … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design
Tagged anamorphosis, Art, Quasiperiodic design, Rotational symmetry
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Rotational symmetry from space with an odd number of dimensions
We now look at the easier case for the post “Quasiperiodic and periodic kaleidoscope from higher dimensional space“, where the embedding space has an odd number of dimensions, p=2q+1. The unit vectors lie at equal angles and form a star … Continue reading
Posted in Kaleidoscopes, programming, Quasiperiodic design
Tagged 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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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