Breaking the rotational symmetry in the dualization method

We now proceed as we did earlier for the projection method in “breaking the ten-fold rotational symmetry“. The sets of parallel lines are moved alternatingly back and forth from the origin. Thus s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)+plusMinus for even i and s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)-plusMinus for odd i. Using n=5 and plusMinus=0.405 I get a quasiperiodic tiling of 5-fold rotational symmetry:

breakingTenToFive0405Again the positions of the stars of ten rhombs and the points of the projection method agree.

This entry was posted in programming, 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