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Tag Archives: Rotational symmetry
Regular polygons as kaleidoscopes
We are using reflection at the sides of a regular polygon to get a space filling periodic image. Its symmetries depend on the symmetry of the image, which lies inside the polygon. As an example, let us look at the … Continue reading
Posted in Kaleidoscopes, Tilings
Tagged hyperbolic space, mirror symmetry, periodic images, regular polygons, Rotational symmetry
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waves – a browser app for creating quasiperiodic wallpapers
I have made a browser app that lets you create quasiperiodic wallpapers. You find it at http://geometricolor.ch/waves.html . It uses a symmetric superposition of waves as proposed by Frank Farris and presented by Erica Klarreich in the Quantamagazin in “How … Continue reading
further wallpapers for hyperbolic space
An equilateral triangle gives us a kaleidoscope of threefold rotational symmetry. With a square we get twofold rotational symmetry. Would reflection at the sides of other regular polygons too give periodic images with rotational symmetry ? To get an hfold … Continue reading
The rotational and mirror symmetry at the center
In the last post I used mirror symmetry at two crossing straight lines and the related inversion at a circle. The mirror symmetries generate a krotational symmetry for an angle of intersection of π/k. With these symmetries I map any point … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, mirror symmetry, rosette, Rotational symmetry
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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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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