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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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Tag Archives: mirror symmetry
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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Rosettes with another mirror symmetry
Symmetries are important for design because they determine the overall appearance of an image. Rotational symmetry without mirror symmetry makes a dynamical image, whereas additional mirror symmetries give a more static appearance. Generally, an image becomes more abstract if we … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, mirror symmetry, Rotational symmetry
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Rosettes with mirror symmetry
The program for making rosettes offers many possibilities and it is difficult to find something to aim for. As a guide we can use symmetries. Mirror symmetry at the xaxis is a simple example. It makes that the image remains unchanged … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged image processing, mirror symmetry, programming, rosette, Rotational symmetry
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class Kaleidoscope
The class Kaleidoscope collects all mappings needed to make the four periodic kaleidoscopes. We first have to create an object with kaleidoscope=new Kaleidoscope(); and then we can choose one of the kaleidoscopes. With kaleidoscope.chooseRectangle(50,120); we would have a rectangular … Continue reading
Posted in Kaleidoscopes, programming
Tagged kaleidoscope, mirror symmetry, programming, Rotational symmetry
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Geometry of kaleidoscopes with periodic images
About a year ago I explained “how to program an ideal kaleidoscope” to get the same as three mirrors put together. Often, one gets images that are not periodic. They have cut lines with a mismatch between the two sides, … Continue reading
Posted in Kaleidoscopes
Tagged Geometry, kaleidoscope, mirror symmetry, period doubling, periodic images, Rotational symmetry
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