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Tag Archives: Penrose tiling
waves – a browser app for creating quasiperiodic wallpapers
I have made a browser app that lets you create quasiperiodic wallpapers. You find it at http://geometricolor.ch/waves.html . It uses a symmetric superposition of waves as proposed by Frank Farris and presented by Erica Klarreich in the Quantamagazin in “How … Continue reading
Examples of basic fivefold rotational symmetry
Here are some quasiperiodic designs of fivefold rotational symmetry. They relate to the Penrose tiling and use the method of “quasiperiodic patterns of 5fold symmetry …“. For all three images the wave packages for the anamorphic mappings X(x,y) and Y(x,y) use the … Continue reading
checkerboard coloring of quasiperiodic tilings
A long time ago I found a coloring of the rhombs of the AmmannBeenker tiling using two colors such that translations exchange colors, see “twofold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading
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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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 Ammann–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
Is there an optimum near s=0.417 ?
Using s=0.417 instead of s=0.42 in the code of the last post I got a quasiperiodic structure with fewer and smaller gaps than the one shown in “Projection method for 5fold rotational symmetry“. Further decreasing s results in somehow chaotic … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged Penrose tiling, pentagon, pentagram, quasiperiodic Tiling
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Projection method for 5fold rotational symmetry – the code
// ********* use processing 2 **************** you can download from processing.org //———————————————————————————— // this is the main code to generate the image of the previous post // and other related quasiperiodic designs // it is similar to the one shown … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged Penrose tiling, pentagram, processing, programming, Quasiperiodic design
1 Comment
Projection method for 5fold rotational symmetry
I am looking again at projection methods. In the post “breaking the 10fold rotational symmetry” I have destroyed the 10fold rotational symmetry of the five sets of stripes by shifting their positions back or forth. This gave a fivefold rotational … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged Penrose tiling, pentagon, pentagram, Quasiperiodic design, Rotational symmetry
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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