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

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quasiperiodic patterns of 5-fold 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 5-fold symmetry … Continue reading

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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 5-fold …“. Note, that I built the code for odd n, especially n=5. For n=8 we get only four different … Continue reading

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Projection method for 5-fold 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

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Projection method for 5-fold rotational symmetry

I am looking again at projection methods. In the post “breaking the 10-fold rotational symmetry” I have destroyed the 10-fold rotational symmetry of the five sets of stripes by shifting their positions back or forth. This gave a five-fold rotational … Continue reading

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breaking the 10-fold rotational symmetry

We modify the “Projection method for 10-fold 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

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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 … Continue reading

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