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Author Archives: Peter Stampfli
Mirror symmetry and rotational symmetry
To study mirror symmetry at the x-axis together with rotational symmetry we can do similarly as in the earlier post “improved symmetric sum“. Here I prefer to present only the conclusions, which you could get by intuition too. It is important … Continue reading
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
Improved symmetric sum
I’ve found a better way how to write the sums of the posts “Rotational symmetry from space with an odd number of dimensions” and “Rotational symmetry from space with an even number of dimensions“. It is more compact, shows how to calculate … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design, Tilings
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