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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
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 Apollonian gasket as a fractal in tiled hyperbolic space
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Monthly Archives: November 2017
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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Variations on the hyperbolic kaleidoscope
In the last post I have presented a hyperbolic kaleidoscope with two and threefold rotational symmetries. Could we have other rotational symmetries? Yes, we simply move the vertical lines! To get an nfold rotational symmetry the circle has to intersect … Continue reading
Posted in Kaleidoscopes
Tagged hyperbolic space, kaleidoscope, Poincaré plane, Rotational symmetry
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A hyperbolic kaleidoscope
In “creating symmetry” Frank Farris shows a wallpaper for hyperbolic space. He uses the Poincaré plane to project the hyperbolic space to our Euclidean drawing surface. The wallpaper then results from mirror symmetries at vertical lines at x=0 and x=0.5 … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged hyperbolic space, inversive geometry, kaleidoscope, mirror symmetry, Poincaré plane
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Five fold rotational symmetry: Tuning the harmonics
In “better images from higher harmonics ?” I have replaced the basic sine and cosine functions by Fourier series approaching a symmetric triangular wave. This gave images with more details and somewhat smaller bullseyes. Here I want to show similar results … Continue reading