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Tag Archives: kaleidoscope
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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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 quasi-periodic and periodic designs in the two-dimensional plane we first make a periodic decoration of higher dimensional space. Then we cut an infinitely thin two-dimensional 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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3-color 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 2-color symmetry. For 3-color symmetries we … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged Color, color symmetry, kaleidoscope, rose window, Rotational symmetry
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n-fold 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 two-color symmetry
To keep things simple I am creating rosette with six-fold 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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Kaleidoscopes with twofold color symmetry.
A checkerboard is a square lattice with twofold color symmetry. The alternating black and white squares make it more interesting than a simple square lattice. Thus I want to have too some twofold color symmetry for our kaleidoscopes. Farris has done this … Continue reading
Posted in Kaleidoscopes, programming
Tagged color symmetry, kaleidoscope, programming, two-color symmetry
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Rosettes with another mirror symmetry
Symmetries are important for design because they determine the overall appearance of an image. Rotational symmetry without mirror symmetry makes a dynamical image, whereas additional mirror symmetries give a more static appearance. Generally, an image becomes more abstract if we … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, mirror symmetry, Rotational symmetry
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Geometry in color 