Tag Archives: Ammann–Beenker tiling

Morphing between square symmetry and eight fold rotational symmetry

A long time ago in “Crazy graph paper” I have shown a morphing between the square lattice and the quasiperiodic Ammann-Beenker tiling of eight-fold rotational symmetry. We can do similar morphs with mapping functions using waves. The wave vectors (1,0) … Continue reading

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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

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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

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Dualization method for ten-fold rotational symmetry – the code

// this is for the main tab // generates 2n-fold rotational symmetry // can be broken to get n-fold rotational symmetry float unitLength; float xRange,yRange;     // visible coordinates from -(xy)Range to +(xy)Range float sqrt2=sqrt(2.),sqrt05=sqrt(0.5),rt3=sqrt(3.); float small,lineLenghtSquare; Grid grid,gridTwo; void setup(){ … Continue reading

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Dualization method for ten-fold rotational symmetry

We now use the dualization method with grids made of several sets of parallel lines. It is important to take the same grids as earlier for the projection method, see “projection method for ten-fold rotational symmetry” and “Projection method for … 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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Putting the dots and lines together – the code

// create an Ammann-Beenker tiling // needs the code of class Vector, class TPoint, class Tiling and saveImage float unitLength; float xRange,yRange; // visible coordinates from -(xy)Range to +(xy)Range float sqrt2=sqrt(2.),sqrt05=sqrt(0.5); float xShift,yShift; // shifting one grid to get different … Continue reading

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