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.

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