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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
 Fractal tiling of a sphere with octahedral twocolour symmetry
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Category Archives: programming
Color symmetry upon rotation
Now I want to present color symmetry upon rotation for periodic and quasiperiodic 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
Rotational symmetry from space with an odd number of dimensions
We now look at the easier case for the post “Quasiperiodic 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
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 quasiperiodic designs. We want symmetric images and thus we have to see how the scalar product changes … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming, Tilings
Tagged Math, mirror symmetry, Rotational symmetry
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Changing the hue
It has been easy to find special color transformations for 2 and 3color 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
Posted in Kaleidoscopes, programming
Tagged Color, color manipulation, hue, programming
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Color transformation
I am now discussing color transformations for creating kaleidoscopic images with twocolor 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
Posted in Kaleidoscopes, programming
Tagged Colors, false colors, negative image, transformation, twocolor symmetry
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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
Posted in Kaleidoscopes, programming
Tagged color symmetry, kaleidoscope, programming, twocolor symmetry
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How to generate rosettes
A rosette is an image with rotational symmetry. For pfold 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
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged anamorphosis, image processing, programming, Rotational symmetry
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