Category Archives: programming

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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Approximating the logarithm function

I still want fast approximations of the logarithm and the inverse tangent function for my work. I don’t know if they are really needed, but they are nice pillow problems to keep you from ruminating those stupid things happening now. If  x is … Continue reading

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Approximating the exponential function

The garden has frozen over and I have caught a cold. It is hard to do difficult work. Thus I continue to find fast approximations of transcendental functions. This is more fun than solving crossword puzzles. The exponential function is not … Continue reading

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Fast approximations of the sine and cosine functions

I made up the web-page http://bookofgames.ch/fastSin.html to check out the different approximations for sine and cosine functions. Load it and make your own tests. You can use the “save”-function of your browser to download the code, change and use it for … Continue reading

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