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Monthly Archives: September 2013
breaking the 10fold rotational symmetry
We modify the “Projection method for 10fold rotational symmetry“. For details see “Projection method – geometry and maths“. To destroy the symmetry we shift the sets of lines alternatingly away or towards the origin. Until now we set the position … Continue reading
12fold rotational symmetry from projection
I use the “Projection method for 10fold rotational symmetry” with 6 instead of 5 sets of parallel lines, setting “numDirections=6;” in “projection method with polygons – the code“. Then, the program searches for 12pointed stars and gives a quasiperiodic design … Continue reading
overlapping polygons – the code
// You need this code to draw overlapping polygons, such as in // the last post “overlapping polygons”. // It first finds at each point for pairs of lines or connections // with the correct angle between. // Then, as … Continue reading
Overlapping polygons
Looking at the dotpattern we got in “Projection method for 10fold rotational symmetry” we could see rhombs instead of the regular polygons shown in “finding polygons“. These rhombs are overlapping and we need a modified code to get them. To … Continue reading
Projection method with polygons – the code
// ********* use processing 2 **************** you can download from processing.org //———————————————————————————— // this is the main code to generate quasiperiodic designs // similar to the one shown in “Finding polygons” // put this code in the main tab of … Continue reading
Posted in programming, Quasiperiodic design
Tagged processing, programming, Quasiperiodic design
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Class Stripes – the code
// a class for working with stripes/sets of parallel lines // lines defined ba ax+by=shift+k; where k is integer // this makes sets of parallel lines as // used in “projection methodgeometry and maths” // see the post “How to … Continue reading
Finding polygons – the code
// kind of extensions to classes TPoint and Tiling // show points without polygons //———————————————————————————– void tilingShowPointsWithoutPolygons(){ for (int i=0;i<tiling.points.length;i++){ if (tiling.points[i].connections.length<2) tiling.points[i].vec.show(); } } // show regular polygons //———————————————————————————– void tilingShowRegularPolygons(int numberCorners){ // regular polygons … Continue reading
Posted in programming, Quasiperiodic design
Tagged Geometry, processing, programming
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Finding polygons
In the earlier post “projection method for 10fold rotational symmetry” I have shown how to get a quasiperiodic design of dots from sets of parallel lines. You can easily recognize dots that are corners of regular pentagons. But how do … Continue reading
Posted in programming, Quasiperiodic design
Tagged Geometry, network, Penrose tiling, pentagon, programming, Quasiperiodic design
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Setting up the coordinates – the modified code
Here is the code that I am using now to set up the coordinates. It is slightly different from the post “setting up the coordinates“. I put it in a separate tab to make debugging easier. // use this … Continue reading
How to shift the design
In the last post “Projection method – geometry and maths” I forgot to show what the parameters s_i are doing. To get the center of perfect 2nfold rotational symmetry at the origin you have to put s_i=0.5 for all i. … Continue reading