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Tag Archives: Iterative method
Iterative method for the AmmannBeenker tiling – the code
// needs class Vector and saveImage code // for details see Iterative method for the AmmannBeenker tiling using “Vector” Vector a,b,c; float f; void setup(){ size(600,600); f=1./(1.+sqrt(2.)); strokeWeight(2); smooth(); } void draw(){ noLoop(); a=new Vector(10,10); b=new … Continue reading
Posted in programming, Quasiperiodic design
Tagged Ammann–Beenker tiling, Iterative method, processing, programming
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Iterative method for the AmmannBeenker tiling using “Vector”
In the earlier post “An efficient iterative method for the AmmannBeenker tiling” I briefly presented an iterative dissection of rhombs and triangles that gives the AmmannBeenker tiling. In the next post “Iterative method for the AmmannBeenker tiling – the code” I … Continue reading
A tiling with squares and triangles only
One can go to the other extreme and find suitable dissections of the square and the equilateral triangle without rhombs. For the square we get two different compositions of the sides. Thus we need two different kinds of triangles to … Continue reading
A tiling with triangles and rhombs only
We can dissect the rhomb into triangles and rhombs without using squares. This dissection destroys its mirrorsymmetry but leaves the rotational symmetry around its center intact. Together with the dissection of the triangle into rhombs and triangles shown in the … Continue reading
Posted in Tilings
Tagged enantiomorphic, Iterative method, mirror symmetry, quasiperiodic Tiling, Rotational symmetry
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Finding an iteration method for the Stampfli tiling – mission impossible
I have caught a cold. I am not able to do new work and thus I am writing up some old leftovers. It is not possible to find an iteration method for the Stampfli tiling. One finds easily how to … Continue reading
Posted in Tilings
Tagged iteration, Iterative method, quasiperiodic Tiling, Stampfli tiling
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Quasiperiodic tiling with pentagons – the Penrose connection
The last post “A quasiperiodic tiling with pentagons” is close to the original reasoning of Penrose, see the article “Penrose tiling” in Wikipedia. He dissected the Pentagon into six smaller ones and filled the gaps with other tiles. He took … Continue reading
Posted in Tilings
Tagged fractal, Iterative method, Penrose tiling, pentagon, pentagram, quasiperiodic Tiling
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A quasiperiodic tiling with pentagrams
I wanted to eliminate the gaps appearing in the earlier post “Iteration of pentagrams“. The pentagon that surrounds the pentagram should ultimately be filled up with pentagrams of different sizes. The six pentagrams of the earlier iteration scheme are shown … Continue reading
Posted in Tilings
Tagged iteration, Iterative method, Penrose tiling, pentagram, quasiperiodic Tiling
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