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Category Archives: Tilings
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
threecolor rotational symmetry
I found it rather difficult to add threecolor 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 quasiperiodic anamorphic … 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
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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Periodic design with 3fold rotational symmetry from 3dimensional space
Three dimensional space gives a threefold 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 spacediagonal 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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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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Quasiperiodic and periodic kaleidoscopes from higher dimensional space
To get quasiperiodic and periodic designs in the twodimensional plane we first make a periodic decoration of higher dimensional space. Then we cut an infinitely thin twodimensional slice out of this space. This gives a design with rotational symmetry if … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design, Tilings
Tagged kaleidoscope, symmetry
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