Category Archives: Quasiperiodic design

Quasiperiodic design with 8-fold rotational symmetry from 4-dimensional space

Using the recipe of the last post for four-dimensional space (p=4) I got this image of 8-fold rotational symmetry: A center of approximate 8-fold rotational symmetry is near the lower left corner. Large brown patches appear at roughly equal distances. … Continue reading

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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

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quasiperiodic patterns of 5-fold 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 5-fold symmetry … Continue reading

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Rotational symmetry from space with an odd number of dimensions

We now look at the easier case for the post “Quasi-periodic 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

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Quasiperiodic and periodic kaleidoscopes from higher dimensional space

To get quasi-periodic and periodic designs in the two-dimensional plane we first make a periodic decoration of higher dimensional space. Then we cut an infinitely thin two-dimensional slice out of this space. This gives a design with rotational symmetry if … Continue reading

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checkerboard coloring of tiling with 12-fold 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 12-fold rotational symmetry. Again the stars of rhombs have only one color: All squares have the … 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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