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

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Examples of basic five-fold rotational symmetry

Here are some quasi-periodic designs of five-fold rotational symmetry. They relate to the Penrose tiling and use the method of “quasiperiodic patterns of 5-fold symmetry …“. For all three images the wave packages for the anamorphic mappings X(x,y) and Y(x,y) use the … Continue reading

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checkerboard coloring of quasiperiodic tilings

A long time ago I found a coloring of the rhombs of the Ammann-Beenker tiling using two colors such that translations exchange colors, see “two-fold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading

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tired of rhombs ?

Just only rhombs may become tiring. You want to have a quasiperiodic tiling of ten-fold 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

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Dualization method for ten-fold rotational symmetry – the code

// this is for the main tab // generates 2n-fold rotational symmetry // can be broken to get n-fold 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

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Dualization method for ten-fold 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 ten-fold rotational symmetry” and “Projection method for … Continue reading

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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 5-fold rotational symmetry“. Further decreasing s results in somehow chaotic … Continue reading

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