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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 AmmannBeenker tiling of eightfold rotational symmetry. We can do similar morphs with mapping functions using waves. The wave vectors (1,0) … Continue reading
Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
Using the recipe of the last post for fourdimensional space (p=4) I got this image of 8fold rotational symmetry: A center of approximate 8fold rotational symmetry is near the lower left corner. Large brown patches appear at roughly equal distances. … Continue reading
checkerboard coloring of quasiperiodic tilings
A long time ago I found a coloring of the rhombs of the AmmannBeenker tiling using two colors such that translations exchange colors, see “twofold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading
Dualization method for tenfold rotational symmetry – the code
// this is for the main tab // generates 2nfold rotational symmetry // can be broken to get nfold 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
Posted in programming, Quasiperiodic design, Tilings
Tagged Ammann–Beenker tiling, Penrose tiling, processing, programming
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Dualization method for tenfold 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 tenfold rotational symmetry” and “Projection method for … Continue reading
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
Putting the dots and lines together – the code
// create an AmmannBeenker 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
Posted in programming, Quasiperiodic design, Tilings
Tagged Ammann–Beenker tiling, Geometry, processing, programming
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