Category Archives: programming

Rotational symmetry from space with an odd number of dimensions

We now look at the easier case for the post “Quasi-periodic and periodic kaleidoscope from higher dimensional space“, where the embedding space has an odd number of dimensions, p=2q+1. The unit vectors lie at equal angles and form a star … 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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Changing the hue

It has been easy to find special color transformations for 2- and 3-color symmetries. For other color symmetries I use a rather general color transformation that changes the hue. First, we separate the pixel color in a grey part and … Continue reading

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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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How to generate rosettes

A rosette is an image with rotational symmetry. For p-fold symmetry we can use the methods of the last post “Anamorphosis and symmetries” with a simple power as a mapping function between output and input images: Here z=x+iy relates to … Continue reading

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Anamorphosis and symmetries

As proposed by Farris in “Creating Symmetry” we can use anamorphosis to make images of any symmetry from some other input image. Here I briefly discuss how I am doing it and what you will find in my next program. Each … Continue reading

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