Tag Archives: mirror symmetry

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 k-rotational symmetry for an angle of intersection of π/k. With these symmetries I map any point … 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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images of 8-fold rotational symmetry and color changing mirror symmetry

Here I am showing some quasi-periodic designs of eight-fold rotational symmetry. They have a color change upon mirroring at the x-axis and 7 other mirror axis generated by the rotational symmetry. Note that these images have a rather large scale … Continue reading

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Examples of basic five-fold rotational symmetry

Here are some quasi-periodic designs of five-fold rotational symmetry. They relate to the Penrose tiling and use the method of “quasiperiodic patterns of 5-fold symmetry …“. For all three images the wave packages for the anamorphic mappings X(x,y) and Y(x,y) use the … Continue reading

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2-color mirror symmetry

We now want an image with periodic or quasi-periodic rotational symmetry that changes colors upon mirroring. Thus we need a color-changing function U(x,y) that changes the sign U(x,-y)=-U(x,y) for its mirror image at the x-axis. We can easily get this … Continue reading

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Mirror symmetry and rotational symmetry

To study mirror symmetry at the x-axis together with rotational symmetry we can do similarly as in the earlier post “improved symmetric sum“. Here I prefer to present only the conclusions, which you could get by intuition too. It is important … Continue reading

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Rotations, mirrorsymmetry and the scalar product

In the last post we have seen that scalar products between a pixel’s position in the output image and certain vectors e define periodic and quasi-periodic designs. We want symmetric images and thus we have to see how the scalar product changes … Continue reading

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