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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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Tag Archives: color symmetry
Fractal tiling of a sphere with octahedral twocolour symmetry
The octahedron can have a nice twocolour symmetry. We get it from putting two tetrahedrons together, making a stellated octahedron. It is an eightpointed star and has already been discussed by Pacioli in his book “de divina proportione” in the … Continue reading
Posted in Fractals, Kaleidoscopes, Selfsimilarity, Tilings
Tagged color symmetry, fractal, kaleidoscope, octahedron, spherical tiling
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Color symmetry using the length scale of the inflated lattice
I have shown some images with 2color symmetry upon rotation shown in “images of 10fold rotational …“. But the fast color changes they hacked them into small pieces. We can get better images if we use a color changing function with … Continue reading
images of 8fold rotational symmetry and color changing mirror symmetry
Here I am showing some quasiperiodic designs of eightfold rotational symmetry. They have a color change upon mirroring at the xaxis and 7 other mirror axis generated by the rotational symmetry. Note that these images have a rather large scale … Continue reading
images of 10fold rotational symmetry and 2color symmetry upon rotation
Here are some images of 10fold rotational symmetry and 2color symmetry upon rotation. They have an additional mirror symmetry. Thus you can discover local mirror symmetries with and without color change. Again, they are of large size and you can … Continue reading
Posted in Quasiperiodic design
Tagged color symmetry, Quasiperiodic design, Rotational symmetry
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2color mirror symmetry
We now want an image with periodic or quasiperiodic rotational symmetry that changes colors upon mirroring. Thus we need a colorchanging function U(x,y) that changes the sign U(x,y)=U(x,y) for its mirror image at the xaxis. We can easily get this … Continue reading
Improved twocolor symmetry upon rotation
As discussed in the post “twocolor rotational symmetry” we get only a single real colorchanging function U(x,y) instead of a mapping W(x,y)=U(x,y)+iV(x,y) to the complex plane. Thus we need a special approach to get a mapping to the input image … Continue reading
improved combination of color symmetry and rotation
As mentioned in the last post using two unrelated anamorphic mappings, one for reading the input image and another one for choosing color variants, makes it difficult to create interesting images. From the mapping that determines the color variant we … Continue reading