Monthly Archives: May 2012

Exhibition of the self-similarity of the tiling

In the last post, I claimed that the tiling one gets from two hexagon-grids is self-similar. But this is not clear from the image I have shown because it has only about 2000 tiles. This is not enough. Just look … Continue reading

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A tiling of 12-fold rotational symmetry from two hexagon grids

We do similarly as in our earlier post “An easy way to quasiperiodic tilings” but now we use grids of hexagons instead of squares. A hexagon has six-fold rotational symmetry and remains unchanged if we rotate it by 60 degrees. … Continue reading

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Doing without octagons

In the last post a presented a rather complicated iteration scheme with squares, rhombs and octagons. We can do without the octagons because an octagon can easily be decomposed into squares and rhombs. Unfortunately, this decomposition lacks symmetry. In this … Continue reading

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A tiling of octagons, squares and rhombs

To find iterative methods is an amusing pastime. While shopping with wife and daughter I found a nice decomposition of rhombs, squares and octagons. Their sides are then reduced by the factor 2+sqrt(2) = 3.14, which is not related to … Continue reading

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Twofold color symmetry in translation – revisited

In my earlier post “twofold color symmetry in translation” I used that the projection method defines four indices for each corner point of the tiles. The sum of the indices is either an odd or even number. Accordingly, the points … Continue reading

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An efficient iterative method for the Ammann-Beenker tiling

Iterative methods are often very fast and easy to program. But the Amman-Beenker tiling (see my earlier post) seems at first sight to be too complicated as a rhomb or a square has to be divided into more than 20 … 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 … 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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