Category Archives: Tilings

Trying to understand “Creating Symmetry”

I am struggling with the book: “Creating Symmetry – The Artful Mathematics of Wallpaper Patterns” by Frank A Farris, which I presented in my last post. As a very pedestrian mathematician and programmer I have difficulties with his abstract methods, based on complex … Continue reading

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Creating Symmetry

Recently I found a very exciting book: “Creating Symmetry – The Artful Mathematics of Wallpaper Patterns” by Frank A Farris. It has many beautiful images and explains the mathematics behind them very well, such that you could do your own work. His … Continue reading

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checkerboard coloring of tiling with 12-fold rotational symmetry

At the risk of boring you I am showing the results of the checkerboard coloring as discussed in the last post, but now for 12-fold rotational symmetry. Again the stars of rhombs have only one color: All squares have the … Continue reading

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checkerboard coloring of quasiperiodic tilings

A long time ago I found a coloring of the rhombs of the Ammann-Beenker tiling using two colors such that translations exchange colors, see “two-fold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading

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tired of rhombs ?

Just only rhombs may become tiring. You want to have a quasiperiodic tiling of ten-fold rotational symmetry with other tiles ? Well, we can easily find a different decoration of a tiling such as the one shown in “Dualization method … Continue reading

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smooth images with the pdf-renderer

The images of the tilings look good on the computer screen but not so if printed out. We do not want to see pixels on paper. We could remedy this using roughly 16 times as much pixels, because the computer … Continue reading

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tiling with rhombs of 12-fold rotational symmetry

If we use n=3 in “Dualization method for ten-fold rotational symmetry – the code” we get the well-known periodic tiling with rhombs of 60 degree acute angle and hexagonal symmetry. It is useful for isometric projections, see the geometricon.wordpress.com blog … Continue reading

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