Tag Archives: Tiling

class Point

For the dualization method we need a better data structure than for the projection method. Thus I defined a new class “Point” to represent grid-points and dual-points. It is an improved version of the class “TPoint”, see “TPoint – the … Continue reading

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Tilings and their duals

I briefly discussed the dualization method in “The dualization method” but you will need more details to be able to understand my computer code. You can find some interesting ideas in Wolfram MathWorld and in Oracle ThinkQuest. In part I … Continue reading

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Iteration of rhombs: the programming code

//  this is the processing code for the iteration of rhombs //  you can reproduce my results of the earlier posts //  feel free to experiment ! // //  to run it you have first to download “processing” from processing.org … Continue reading

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More results from the iteration of rhombs

Iterative methods can give many different results with only some small changes. An example is the iteration of rhombs to create a tiling with eight-fold rotational symmetry, see my post “Iteration of rhombs”. Here we can use different angles for … Continue reading

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Why these tilings are not periodic

Often, you can put together two periodic patterns of different length and you get a new pattern, which is periodic too. The length of the period of the joint pattern is the least common multiple of the period lengths of … Continue reading

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Another variation on the Amman-Beenker tiling

Trying to get something new I used a grid of greater squares of length L=sqrt(2.) and a distance of 1 between their centers. This makes overlapping squares. Using two such grids as before (see “An easy way to quasiperiodic tilings“) … Continue reading

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Another tiling of eight-fold rotational symmetry

I am using the same basic method as for the Amman-Beenker tiling, see my post “How to find these corner points of the tiles“, but now with smaller squares. The distance between the centers of the squares remains equal to 1, … Continue reading

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