Monthly Archives: September 2013

breaking the 10-fold rotational symmetry

We modify the “Projection method for 10-fold 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

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12-fold rotational symmetry from projection

I use the “Projection method for 10-fold 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 12-pointed stars and gives a quasiperiodic design … Continue reading

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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

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Overlapping polygons

Looking at the dot-pattern we got in “Projection method for 10-fold 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

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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

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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 method-geometry and maths” // see the post “How to … Continue reading

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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

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