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

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Variations on the hyperbolic kaleidoscope

In the last post I have presented a hyperbolic kaleidoscope with two- and three-fold rotational symmetries. Could we have other rotational symmetries? Yes, we simply move the vertical lines! To get an n-fold rotational symmetry the circle has to intersect … Continue reading

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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

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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 bulls-eyes. Here I want to show similar results … Continue reading

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