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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Tag Archives: Quasiperiodic design
Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
We now want to impose inversion symmetry in addition to rotational symmetry on our designs. This means that the mapping functions should not change upon inversion of the position. Thus X(x,y)=X(x,y) and Y(x,y)=Y(x,y). Let’s consider space with an odd number … Continue reading
quasiperiodic patterns of 5fold symmetry from 5 dimensional space
I now want to see some images. Using a photo of a caterpillar as input image I get I used the simplest quasiperiodic mapping functions resulting from the theory of the last post and The center of perfect 5fold symmetry … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design
Tagged anamorphosis, Art, Quasiperiodic design, Rotational symmetry
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experiment with the projection method
It seems to be foolish to use an even number, such as n=8, in the code of “projection method for 5fold …“. Note, that I built the code for odd n, especially n=5. For n=8 we get only four different … Continue reading
Projection method for 5fold rotational symmetry – the code
// ********* use processing 2 **************** you can download from processing.org //———————————————————————————— // this is the main code to generate the image of the previous post // and other related quasiperiodic designs // it is similar to the one shown … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged Penrose tiling, pentagram, processing, programming, Quasiperiodic design
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Projection method for 5fold rotational symmetry
I am looking again at projection methods. In the post “breaking the 10fold rotational symmetry” I have destroyed the 10fold rotational symmetry of the five sets of stripes by shifting their positions back or forth. This gave a fivefold rotational … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged Penrose tiling, pentagon, pentagram, Quasiperiodic design, Rotational symmetry
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breaking the 10fold rotational symmetry
We modify the “Projection method for 10fold rotational symmetry“. For details see “Projection method – geometry and maths“. To destroy the symmetry we shift the sets of lines alternatingly away or towards the origin. Until now we set the position … Continue reading
12fold rotational symmetry from projection
I use the “Projection method for 10fold 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 12pointed stars and gives a quasiperiodic design … Continue reading