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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
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 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Monthly Archives: August 2013
Projection method and corner points – the code
float unitLength; float xRange,yRange; // visible coordinates from (xy)Range to +(xy)Range float xShift,yShift; // shifting one grid to get different parts of the tiling float sqrt2=sqrt(2.),sqrt05=sqrt(0.5); void setup(){ size(600,600); smooth(); unitLength=30; xShift=0.01; yShift=0.05; ellipseMode(CENTER); … Continue reading
Posted in programming
Tagged Ammann–Beenker tiling, processing, programming, quasiperiodic Tiling
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Projection method and corner points
Earlier I showed you how get the corner points of a quasiperiodic tiling. For the AmmannBeenker tiling see the posts “An easy way to quasiperiodic tilings” and “How to find these corner points of the tiles“. This is easy to … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged Ammann–Beenker tiling, programming, quasiperiodic Tiling
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Setting up the coordinates
Computer technology determines the coordinates that processing uses. The distance between two pixels is the unit length and the origin lies at the upper left corner. This is not what we need in geometry and mathematics. Fortunately, processing has all … Continue reading
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
class Vector – the code
// a class for twodimensional vectors, similarly as PVector //———————————————————— // // some important values float vectorSmall=0.0001,vectorSqrt05=sqrt(0.5); float vectorDiameter=8; color vectorColor=color(255); //rgb mode, for green // and here’s the class class Vector{ float x,y; // create a … Continue reading
class Vector
The basic element of geometry is a point or vector. We could use the PVector class of processing to work with vectors in 2 and 3dimensional space. However, this is not really efficient for 2dimensional vectors, because their zcomponent is … Continue reading