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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
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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
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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
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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
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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
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