
Recent Posts
Recent Comments
Archives
 September 2019
 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
Tag Archives: Math
Bridges 2018 Stockholm
I have been at the Bridges 2018 conference in Stockholm to present my work on kaleidoscopes. My paper “Kaleidoscopes for NonEuclidean Space” has more details than this blog and is more coherent. The Bridges Organization, which promotes connections between mathematics … Continue reading
Rotations, mirrorsymmetry and the scalar product
In the last post we have seen that scalar products between a pixel’s position in the output image and certain vectors e define periodic and quasiperiodic designs. We want symmetric images and thus we have to see how the scalar product changes … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming, Tilings
Tagged Math, mirror symmetry, Rotational symmetry
Leave a comment
How to calculate the corner points and the projection method
Again something for the more mathematically minded. I am discussing here some important details on the earlier post “A tiling of 12fold rotational symmetry …” . Actually, these calculations are similar as in the earlier post “How to find these … Continue reading
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
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
Another tiling of eightfold rotational symmetry
I am using the same basic method as for the AmmanBeenker 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
Posted in Tilings
Tagged Art, Color, Math, Rotational symmetry, Tessellation, Tiling, translational symmetry
Leave a comment
The basic AmmanBeenker tiling
With the details presented in the earlier posts we can easily get large parts of this tiling. I have tried to choose colors, which are not too contrasting and too hard on the eyes: We see that small patterns are … Continue reading
Posted in Tilings
Tagged fractal, Geometry, Math, Quasiperiodicity, Recreation, Tessellation, Tile, Tiling
Leave a comment