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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Tag Archives: kaleidoscope
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 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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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 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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3color symmetry
For color symmetries we need a mapping W(z) for its structure as discussed in the last post and some suitable color transformations. In an earlier post I discussed some simple transformations for making a 2color symmetry. For 3color symmetries we … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged Color, color symmetry, kaleidoscope, rose window, Rotational symmetry
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nfold color symmetry
Let’s begin with a simple kaleidoscope, where a pixel at coordinates z=x+iy has the original colors of an input image at the mapped coordinates Z(z)=X(x,y)+iY(x,y). It has some symmetry s. It is a mapping of the plane that does not … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, color symmetry, kaleidoscope, programming, Rotational symmetry
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Simple example of a rosette with twocolor symmetry
To keep things simple I am creating rosette with sixfold rotational symmetry. The mapping functions are, using polar coordinates: X = r³ cos(6*φ) and Y = r³ sin(6*φ). An input image of a single butterfly results in 6 distorted butterflies: The black … Continue reading
Posted in Kaleidoscopes
Tagged color symmetry, kaleidoscope, rose window, Rotational symmetry
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