Iterative method for the Ammann-Beenker tiling using “Vector”

In the earlier post “An efficient iterative method for the Ammann-Beenker tiling” I briefly presented an iterative dissection of rhombs and triangles that gives the Ammann-Beenker tiling. In the next post “Iterative method for the Ammann-Beenker tiling – the code” I will publish the corresponding computer program. Note that it uses the class Vector and saveImage code.

The vectors for the dissection of the triangle are:trianglePlus

Note that the diagonal of a square is sqrt(2) times its side. Thus we get the important ratio f=1/(1+sqrt(2)).

The vectors for the dissection of the rhomb are:rhombPlus

Using good old Pythagoras we get that the long diagonal of the rhomb is sqrt(2+sqrt(2)) times its side and the small diagonal sqrt(2-sqrt(2)) times its side. This is used in the calculations for za and zd.

Finally the program should give you this result:

tiling

See how easy this is to program and feel free to do your own experiments.

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