Tag Archives: quasiperiodic Tiling

three-color rotational symmetry

I found it rather difficult to add three-color symmetry to rotational symmetry and had to do the theory of the post “color symmetry upon rotation“. Then, programming was quite easy.  In the end we combine a periodic or quasi-periodic anamorphic … Continue reading

Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design, Tilings | Tagged , , , , | Leave a comment

Quasiperiodic design with 8-fold rotational symmetry from 4-dimensional space

Using the recipe of the last post for four-dimensional space (p=4) I got this image of 8-fold rotational symmetry: A center of approximate 8-fold rotational symmetry is near the lower left corner. Large brown patches appear at roughly equal distances. … Continue reading

Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design | Tagged , , , | Leave a comment

checkerboard coloring of tiling with 12-fold rotational symmetry

At the risk of boring you I am showing the results of the checkerboard coloring as discussed in the last post, but now for 12-fold rotational symmetry. Again the stars of rhombs have only one color: All squares have the … Continue reading

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

checkerboard coloring of quasiperiodic tilings

A long time ago I found a coloring of the rhombs of the Ammann-Beenker tiling using two colors such that translations exchange colors, see “two-fold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading

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

tired of rhombs ?

Just only rhombs may become tiring. You want to have a quasiperiodic tiling of ten-fold rotational symmetry with other tiles ? Well, we can easily find a different decoration of a tiling such as the one shown in “Dualization method … Continue reading

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

tiling with rhombs of 12-fold rotational symmetry

If we use n=3 in “Dualization method for ten-fold rotational symmetry – the code” we get the well-known periodic tiling with rhombs of 60 degree acute angle and hexagonal symmetry. It is useful for isometric projections, see the geometricon.wordpress.com blog … Continue reading

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

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 … Continue reading

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