Tag Archives: mirror symmetry

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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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

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waves

I was looking at the waves resulting from stones thrown into a lake. This made me think of an anamorphosis, that simulates these troubled reflections. It is actually quite simple. The center of the coordinate system is in the middle. … Continue reading

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