Tag Archives: Iterative method

Iterative method for the Ammann-Beenker tiling – the code

// needs class Vector and saveImage code // for details see Iterative method for the Ammann-Beenker 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

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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 … Continue reading

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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

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A tiling with triangles and rhombs only

We can dissect the rhomb into triangles and rhombs without using squares. This dissection destroys its mirror-symmetry 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

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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 left-overs. It is not possible to find an iteration method for the Stampfli tiling. One finds easily how to … Continue reading

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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

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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

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