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Monthly Archives: May 2012
Exhibition of the selfsimilarity of the tiling
In the last post, I claimed that the tiling one gets from two hexagongrids is selfsimilar. 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
Posted in Selfsimilarity, Tilings
Tagged Geometry, Math, quasiperiodic Tiling, Quasiperiodicity, Selfsimilarity
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A tiling of 12fold 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 sixfold rotational symmetry and remains unchanged if we rotate it by 60 degrees. … Continue reading
Posted in Tilings
Tagged Art, Geometry, quasiperiodic Tiling, Quasiperiodicity, Rotational symmetry
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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
Posted in Tilings
Tagged Art, fractal, fractal design, Iterative method, quasiperiodic Tiling, Tessellation
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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
Posted in Tilings
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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
Posted in Tilings
Tagged Art, Iterative method, quasiperiodic Tiling, Tessellation, translational symmetry
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An efficient iterative method for the AmmannBeenker tiling
Iterative methods are often very fast and easy to program. But the AmmanBeenker 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
Posted in Tilings
Tagged Art, iteration, Iterative method, quasiperiodic Tiling, Quasiperiodicity, Rotational symmetry, Tessellation
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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
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 eightfold rotational symmetry, see my post “Iteration of rhombs”. Here we can use different angles for … Continue reading
Posted in Fractals, Tilings
Tagged Art, fractal, Iterative method, programming, Rotational symmetry, Tiling
2 Comments