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Tag Archives: Quasiperiodic design
Mirror symmetry and rotational symmetry
To study mirror symmetry at the xaxis 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 couldĀ get by intuition too. It is important … 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
twocolor rotational symmetry
We can only add a twocolor 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 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
Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
We now want to impose inversion symmetry in addition to rotational symmetry on our designs. This means that the mapping functions should not change upon inversion of the position. Thus X(x,y)=X(x,y) and Y(x,y)=Y(x,y). Let’s consider space with an odd number … Continue reading
quasiperiodic patterns of 5fold symmetry from 5 dimensional space
I now want to see some images. Using a photo of a caterpillar as input image I get I used the simplest quasiperiodic mapping functions resulting from the theory of the last post and The center of perfect 5fold symmetry … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design
Tagged anamorphosis, Art, Quasiperiodic design, Rotational symmetry
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