3-color symmetry

For color symmetries we need a mapping W(z) for its structure as discussed in the last post and some suitable color transformations. In an earlier post I discussed some simple transformations for making a 2-color symmetry. For 3-color symmetries we easily find a fitting transformation using that a pixel has red, green and blue color components. We simply exchange them cyclically – red becomes green, green becomes blue and blue becomes red. Another possibility: red becomes blue, blue becomes green and green becomes red. Together with the original colors we get three color variants as needed.

This 3-color symmetry together with a six-fold rotational symmetry gives results like this:

The mapping of the color symmetry is simply W(z)=z². Here I added a dark border between the different sectors of the color symmetry. Admittedly, this is merely a proof of concept and not very interesting. Color symmetries become more useful in periodic and quasi-periodic kaleidoscopes.

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