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 Color symmetry using the length scale of the inflated lattice
 images with 5fold symmetry and color change indicating selfsimilarity
 images of 8fold rotational symmetry and color changing mirror symmetry
 images of 10fold rotational symmetry and 2color symmetry upon rotation
 Examples of basic fivefold rotational symmetry
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Tag Archives: mirror symmetry
images of 8fold rotational symmetry and color changing mirror symmetry
Here I am showing some quasiperiodic designs of eightfold rotational symmetry. They have a color change upon mirroring at the xaxis and 7 other mirror axis generated by the rotational symmetry. Note that these images have a rather large scale … Continue reading
Examples of basic fivefold rotational symmetry
Here are some quasiperiodic designs of fivefold rotational symmetry. They relate to the Penrose tiling and use the method of “quasiperiodic patterns of 5fold symmetry …“. For all three images the wave packages for the anamorphic mappings X(x,y) and Y(x,y) use the … Continue reading
2color mirror symmetry
We now want an image with periodic or quasiperiodic rotational symmetry that changes colors upon mirroring. Thus we need a colorchanging function U(x,y) that changes the sign U(x,y)=U(x,y) for its mirror image at the xaxis. We can easily get this … Continue reading
Mirror symmetry and rotational symmetry
To study mirror symmetry at the xaxis together with rotational symmetry we can do similarly as in the earlier post “improved symmetric sum“. Here I prefer to present only the conclusions, which you could get by intuition too. It is important … Continue reading
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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Rosettes with glide reflection and rotation symmetry
We now come to the last distinct combination of symmetries for friezes and rosettes. It uses the glide reflection and the rotation by 180 degrees resulting from two mirror symmetries of the two preceeding posts. The mapping functions have to have the symmetry … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged mirror symmetry, rose window, Rotational symmetry
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Combinations of mirror symmetries
We now create rosettes with combinations of the two mirror symmetries. We can put them in “parallel” or in “series”. In “parallel” means that the rosette has both symmetries at the same time and thus the mapping functions have to obey … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged image processing, mirror symmetry, rose window, Rotational symmetry
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