Category Archives: Quasiperiodic design

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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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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Color symmetry using the length scale of the inflated lattice

I have shown some images with 2-color symmetry upon rotation shown in “images of 10-fold 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

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images with 5-fold symmetry and color change indicating self-similarity

And now for more images with 5-fold rotational symmetry and color change derived from self-similarity as discussed in “self-similarity and color modification“. Zoom in to see the molten watch faces in this image: Here I used the portrait of a … 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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images of 10-fold rotational symmetry and 2-color symmetry upon rotation

Here are some images of 10-fold rotational symmetry and 2-color symmetry upon rotation. They have an additional mirror symmetry. Thus you can discover local mirror symmetries with and without color change. Again, they are of large size and you can … 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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