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Tag Archives: kaleidoscope
Improved two-color symmetry upon rotation
As discussed in the post “two-color rotational symmetry” we get only a single real color-changing 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
three-color rotational symmetry
I found it rather difficult to add three-color symmetry to rotational symmetry and had to do the theory of the post “color symmetry upon rotation“. Then, programming was quite easy. In the end we combine a periodic or quasi-periodic anamorphic … Continue reading
two-color rotational symmetry
We can only add a two-color symmetry to a rotational symmetry if the rotational symmetry is of even order. After some simple calculations, we get from the previous post a real mapping for selecting the color variants where the d … Continue reading
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
Rotational symmetry from space with an even number of dimensions
For an embedding space with an even number of dimensions p=2q we do similarly as for an odd number of dimensions, see the earlier post “Rotational symmetry from…“. Note that now we should not use an angle of 2π/p between … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, Rotational symmetry
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Periodic design with 3-fold rotational symmetry from 3-dimensional space
Three dimensional space gives a three-fold rotational symmetry in the drawing plane. The designs are periodic. Note that if you put a cube on one of its points and look along its space-diagonal from above, then you see an object with … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Tilings
Tagged kaleidoscope, Rotational symmetry, translational symmetry
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