
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: dual tesselation
Dualization method for tenfold rotational symmetry
We now use the dualization method with grids made of several sets of parallel lines. It is important to take the same grids as earlier for the projection method, see “projection method for tenfold rotational symmetry” and “Projection method for … Continue reading
irregular tilings and their duals
To get a better idea how the dualization method works we look at the same hexagonal tiling as before. Here is an image, where the triangles of the dual tiling are shaded: We now add a line to the original … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged dual tesselation, quasiperiodic Tiling, Tessellation
Leave a comment
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
Posted in Tilings
Tagged dual, dual tesselation, dualization, network, Tessellation, Tiling
Leave a comment
Cellular automaton on quasiperiodic tiling
Any tiling can be used to define a cellular automaton. The tiles (squares, triangles, rhombs and other polygons) are simply the cells. Each tile has all other tiles with a common edge in its von Neumann neighborhood. I use the … Continue reading
Doubling the tessellation of triangles and squares with twofold rotational symmetry
This is rather for the completeness sake: The last semiregular tessellation I have not yet used to get a quasiperiodic tiling. It has squares and triangles, as has another tessellation with fourfold rotational symmetry, see “Doubling the tessellation of squares … Continue reading
Posted in Tilings
Tagged dual tesselation, quasiperiodic Tiling, Rotational symmetry
Leave a comment
Doubling the semiregular tesselation of hexagons and many triangles
There is one semiregular tessellation of sixfold rotational symmetry left over which I have not yet used to create a quasiperiodic tiling of 12fold rotational symmetry. It has rings of triangles such that the hexagons do not touch each other, … Continue reading
Beautifying the double grid
The grids for quasiperiodic tilings do not look good because a lot of irregular shapes arise from superimposing two simple grids, see the article “Doubling the tessellation of triangles“. But we can distort these double grids and get new interesting … Continue reading
Posted in Tilings
Tagged Ammannâ€“Beenker tiling, dual tesselation, Geometry, islamic art, quasiperiodic Tiling, Stampfli tiling
Leave a comment