Monthly Archives: June 2012

Morphing the Ammann-Beenker tiling

We can vary the dualization method in many ways. Here we play with the Ammann-Beenker tiling and use different lengths for the lines generated by the first square grid and the second square grid. This produces squares of different sizes … Continue reading

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Morphing the tiling of octagons and squares

In the last post “Doubling the tessellation of octagons and squares” I have used a grid of squares (in black) with diagonals (in blue). The blue lines are distinct and cannot be mapped onto the black lines by the symmetries … Continue reading

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Doubling the tessellation of octagons and squares

Regular octagons and squares make up a well-known semiregular tessellation that is often used to decorate floors Its dual grid is essentially a square grid with diagonal lines added. Four lines cross at the corner points giving the octagons of … Continue reading

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The dualization method

In this post I am presenting a third method for producing quasiperiodic tilings. This is rather technical but also very important for the future work in this blog. Note that the projection method, the iteration method and the dualization method … Continue reading

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Iteration of rhombs: filling the gap (2)

The gaps in the fractal design of 12-fold rotational symmetry of my earlier post “Iteration of rhombs” can be filled in similarly as for the design of 8-fold rotational symmetry (see the post ” … filling the gap “.) Here … Continue reading

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Two-color symmetry in rotation for the Stampfli tiling.

I want to have two colors for each tile of the quasiperiodic tiling with 12-fold rotational symmetry presented in an earlier post. The colors of the tiles depends on their orientation and they should exchange if the tiling is rotated … Continue reading

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Iteration of rhombs: Filling the gap

In an earlier post “Iteration of rhombs” I got a fractal design of 8-fold rotational symmetry starting with a rhomb of acute angles of 45 degrees. An iterative step then replaces each rhomb by four rhombs, leaving a square gap … Continue reading

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