12-fold rotational symmetry from projection

I use the “Projection method for 10-fold rotational symmetry” with 6 instead of 5 sets of parallel lines, setting “numDirections=6;” in “projection method with polygons – the code“. Then, the program searches for 12-pointed stars and gives a quasiperiodic design with 12-fold rotational symmetry as a projection from 6-dimensional space.

Drawing equilateral triangles and squares I get a rather dull design at small scales. But at very large scales it becomes interesting:

12erAgain, the center of perfect 12-fold rotational symmetry is at the upper right corner. There appear some other irregular polygons as tiles. But there are no large gaps of fractal nature. Thus this might really be a quasiperiodic tiling.

The white dots show points that are not at the corner of polygons. They themselves are corner points of large rhombs, squares, triangles and shield-tiles. Thus we could get another quasiperiodic tiling from these points. But at this very large scale numerical errors could become important and we should use double precision numbers instead of simple float. Also, the simple search for connections between points takes a lot of time and needs to be improved.

This entry was posted in Quasiperiodic design, Tilings and tagged , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s