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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
 Fractal tiling of a sphere with octahedral twocolour symmetry
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Tag Archives: rose window
Further hyperbolic kaleidoscopes
In the last post I have used reflections at two parallel lines and a circle to get a Poincaré plane that shows a periodic decoration of hyperbolic space. What happens if the straight lines are not parallel and intersect? Then … Continue reading
Posted in Kaleidoscopes
Tagged hyperbolic space, kaleidoscope, Poincaré disc, rose window, Rotational 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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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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Rosettes with glide reflection and rotation symmetry
We now come to the last distinct combination of symmetries for friezes and rosettes. It uses the glide reflection and the rotation by 180 degrees resulting from two mirror symmetries of the two preceeding posts. The mapping functions have to have the symmetry … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged mirror symmetry, rose window, Rotational symmetry
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rosettes with glide reflection
For a rosette of pfold rotational symmetry you have an equivalent to the glide reflection symmetry of a fries. It is a rotation by an angle of π/p around its center together with a reflection or rather inversion at r=1. … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, rose window, Rotational symmetry
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Combinations of mirror symmetries
We now create rosettes with combinations of the two mirror symmetries. We can put them in “parallel” or in “series”. In “parallel” means that the rosette has both symmetries at the same time and thus the mapping functions have to obey … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged image processing, mirror symmetry, rose window, Rotational symmetry
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tired of rhombs ?
Just only rhombs may become tiring. You want to have a quasiperiodic tiling of tenfold rotational symmetry with other tiles ? Well, we can easily find a different decoration of a tiling such as the one shown in “Dualization method … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged Geometry, ornament, Penrose tiling, programming, quasiperiodic Tiling, rose window
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