Category Archives: Kaleidoscopes

Color transformation

I am now discussing color transformations for creating kaleidoscopic images with two-color symmetry. Each pixel has three color components: red, green and blue. Their values are between 0 and 255. Thus we can think that a pixel color is a point with … Continue reading

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Kaleidoscopes with twofold color symmetry.

A checkerboard is a square lattice with twofold color symmetry. The alternating black and white squares make it more interesting than a simple square lattice. Thus I want to have too some twofold color symmetry for our kaleidoscopes. Farris has done this … 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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rosettes with glide reflection

For a rosette of p-fold rotational symmetry you have an equivalent to the glide reflection symmetry of a fries. It is a rotation by an angle of π/p around its center together with a reflection or  rather inversion at r=1. … 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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