
Recent Posts
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
 Apollonian gasket as a spherical fractal with tetrahedral symmetry
 waves – a browser app for creating quasiperiodic wallpapers
Recent Comments
Archives
 August 2019
 July 2019
 April 2019
 March 2019
 November 2018
 October 2018
 September 2018
 August 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 February 2017
 January 2017
 November 2016
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
Categories
Meta
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
Leave a comment
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
2 Comments
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
Leave a comment
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
Leave a comment
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
Leave a comment
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
Leave a comment
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