Tag Archives: mirror symmetry

Mirror symmetry and rotational symmetry

To study mirror symmetry at the x-axis 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

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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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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

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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

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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

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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 x-axis is a simple example. It makes that the image remains unchanged … Continue reading

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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

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