Category Archives: Anamorphosis

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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Rotational symmetry from space with an even number of dimensions

For an embedding space with an even number of dimensions p=2q we do similarly as for an odd number of dimensions, see the earlier post “Rotational symmetry from…“. Note that now we should not use an angle of 2π/p between … Continue reading

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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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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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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 quasi-periodic designs. We want symmetric images and thus we have to see how the scalar product changes … 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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