Category Archives: programming

Five fold rotational symmetry: Tuning the harmonics

In “better images from higher harmonics ?” I have replaced the basic sine and cosine functions by Fourier series approaching a symmetric triangular wave. This gave images with more details and somewhat smaller bulls-eyes. Here I want to show similar results … Continue reading

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Smoothing images

The image quality suffers if the mapping functions X(x,y) and Y(x,y) of the position (x,y) of a pixel of the output image to the position (X,Y) of the sampled input image pixel are strongly contracting or expanding. For contracting mappings … Continue reading

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Better images from higher harmonics ?

Maybe you have noticed that a lot of round shapes without details in the recent images of this blog. They resemble bulls-eyes. Here is an example: It’s a periodic image with square symmetry and no mirror symmetry. Its big grey … Continue reading

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Color symmetry upon rotation

Now I want to present color symmetry upon rotation for periodic and quasi-periodic kaleidoscopes. We have n different versions how to show the pixel colors of the input image in the new output image. For a color symmetry we have … Continue reading

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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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