Tag Archives: quasiperiodic Tiling

Breaking the rotational symmetry in the dualization method

We now proceed as we did earlier for the projection method in “breaking the ten-fold rotational symmetry“. The sets of parallel lines are moved alternatingly back and forth from the origin. Thus s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)+plusMinus for even i and s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)-plusMinus for odd … Continue reading

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Dualization method for ten-fold rotational symmetry

We now use the dualization method with grids made of several sets of parallel lines. It is important to take the same grids as earlier for the projection method, see “projection method for ten-fold rotational symmetry” and “Projection method for … Continue reading

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dualization method for the Stampfli tiling – the code

// ********* use processing 2 **************** you can download from processing.org //———————————————————————————— // this is the main code to generate the Stampfli tiling // it shows you how to use the dualization method, // you can generate other tilings with … Continue reading

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Dualization method for the Stampfli tiling

I am now showing step by step how to get the Stampfli tiling with the dualization method. In the next post you will find the code, which you could change to make other quasiperiodic tilings. First, we combine two hexagon … Continue reading

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irregular tilings and their duals

To get a better idea how the dualization method works we look at the same hexagonal tiling as before. Here is an image, where the triangles of the dual tiling are shaded: We now add a line to the original … Continue reading

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Projection method for the Stampfli and the Socolar tiling

In “A tiling of 12-fold rotational symmetry from two hexagon grids” and following posts I have already discussed the projection method for the Stampfli tiling. It is quite similar to the projection method for the Ammann-Beenker tiling. But there is … Continue reading

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experiment with the projection method

It seems to be foolish to use an even number, such as n=8, in the code of “projection method for 5-fold …“. Note, that I built the code for odd n, especially n=5. For n=8 we get only four different … Continue reading

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