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Tag Archives: Rotational symmetry
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
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
Color symmetry using the length scale of the inflated lattice
I have shown some images with 2color symmetry upon rotation shown in “images of 10fold rotational …“. But the fast color changes they hacked them into small pieces. We can get better images if we use a color changing function with … Continue reading
images with 5fold symmetry and color change indicating selfsimilarity
And now for more images with 5fold rotational symmetry and color change derived from selfsimilarity as discussed in “selfsimilarity and color modification“. Zoom in to see the molten watch faces in this image: Here I used the portrait of a … Continue reading