Tag Archives: dual tesselation

Dualization method for ten-fold 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 ten-fold rotational symmetry” and “Projection method for … Continue reading

Posted in programming, Quasiperiodic design, Tilings | Tagged , , , , , , | Leave a comment

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 , , | 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 , , , , , | 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

Posted in Cellular automata, Tilings | Tagged , , , , , , | Leave a comment

Doubling the tessellation of triangles and squares with two-fold 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 four-fold rotational symmetry, see “Doubling the tessellation of squares … Continue reading

Posted in Tilings | Tagged , , | Leave a comment

Doubling the semiregular tesselation of hexagons and many triangles

There is one semiregular tessellation of six-fold rotational symmetry left over which I have not yet used to create a quasiperiodic tiling of 12-fold rotational symmetry. It has rings of triangles such that the hexagons do not touch each other, … Continue reading

Posted in Tilings | Tagged , , | Leave a comment

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 , , , , , | Leave a comment