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Monthly Archives: November 2013
tired of rhombs ?
Just only rhombs may become tiring. You want to have a quasiperiodic tiling of tenfold rotational symmetry with other tiles ? Well, we can easily find a different decoration of a tiling such as the one shown in “Dualization method … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged Geometry, ornament, Penrose tiling, programming, quasiperiodic Tiling, rose window
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smooth images with the pdfrenderer
The images of the tilings look good on the computer screen but not so if printed out. We do not want to see pixels on paper. We could remedy this using roughly 16 times as much pixels, because the computer … Continue reading
Posted in Extra, programming, Quasiperiodic design, Tilings
Tagged Geometry, pdf, processing, programming, smoothing images
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tiling with rhombs of 12fold rotational symmetry
If we use n=3 in “Dualization method for tenfold rotational symmetry – the code” we get the wellknown periodic tiling with rhombs of 60 degree acute angle and hexagonal symmetry. It is useful for isometric projections, see the geometricon.wordpress.com blog … Continue reading
Breaking the rotational symmetry in the dualization method
We now proceed as we did earlier for the projection method in “breaking the tenfold rotational symmetry“. The sets of parallel lines are moved alternatingly back and forth from the origin. Thus s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)+plusMinus for even i and s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)plusMinus for odd … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged quasiperiodic Tiling, Rotational symmetry
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Dualization method for tenfold rotational symmetry – the code
// this is for the main tab // generates 2nfold rotational symmetry // can be broken to get nfold rotational symmetry float unitLength; float xRange,yRange; // visible coordinates from (xy)Range to +(xy)Range float sqrt2=sqrt(2.),sqrt05=sqrt(0.5),rt3=sqrt(3.); float small,lineLenghtSquare; Grid grid,gridTwo; void setup(){ … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged Ammannâ€“Beenker tiling, Penrose tiling, processing, programming
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Dualization method for tenfold rotational symmetry
We now use the dualization method with grids made of several sets of parallel lines. It is important to take the same grids as earlier for the projection method, see “projection method for tenfold rotational symmetry” and “Projection method for … Continue reading
Problem in “combination of grids – the code”
I tried to follow Eric (see his comments on “dualization method for the Stampfli tiling“). But the program crashed sometimes because it generated grid lines with endpoints that are both the same and length equal to zero. There seems to … Continue reading