
Recent Posts
Recent Comments
Archives
 September 2019
 August 2019
 July 2019
 April 2019
 March 2019
 November 2018
 October 2018
 September 2018
 August 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 February 2017
 January 2017
 November 2016
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
Categories
Meta
Category Archives: Quasiperiodic design
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
Five fold rotational symmetry: Tuning the harmonics
In “better images from higher harmonics ?” I have replaced the basic sine and cosine functions by Fourier series approaching a symmetric triangular wave. This gave images with more details and somewhat smaller bullseyes. Here I want to show similar results … Continue reading
Color symmetry using the length scale of the inflated lattice
I have shown some images with 2color symmetry upon rotation shown in “images of 10fold rotational …“. But the fast color changes they hacked them into small pieces. We can get better images if we use a color changing function with … Continue reading
images with 5fold symmetry and color change indicating selfsimilarity
And now for more images with 5fold rotational symmetry and color change derived from selfsimilarity as discussed in “selfsimilarity and color modification“. Zoom in to see the molten watch faces in this image: Here I used the portrait of a … Continue reading
images of 8fold rotational symmetry and color changing mirror symmetry
Here I am showing some quasiperiodic designs of eightfold rotational symmetry. They have a color change upon mirroring at the xaxis and 7 other mirror axis generated by the rotational symmetry. Note that these images have a rather large scale … Continue reading
images of 10fold rotational symmetry and 2color symmetry upon rotation
Here are some images of 10fold rotational symmetry and 2color symmetry upon rotation. They have an additional mirror symmetry. Thus you can discover local mirror symmetries with and without color change. Again, they are of large size and you can … Continue reading
Posted in Quasiperiodic design
Tagged color symmetry, Quasiperiodic design, Rotational symmetry
Leave a comment
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
Morphing between square symmetry and eight fold rotational symmetry
A long time ago in “Crazy graph paper” I have shown a morphing between the square lattice and the quasiperiodic AmmannBeenker tiling of eightfold rotational symmetry. We can do similar morphs with mapping functions using waves. The wave vectors (1,0) … Continue reading
Selfsimilarity and color modification
The Penrose tiling is selfsimilar as many other quasiperiodic tilings. It matches a copy of itself inflated by the golden ratio τ=(1+√5)/2≅1.618, see “Penrose tiling tied up in ribbons“. Noting that our quasiperiodic designs of 5fold symmetry are closely related to … Continue reading
2color mirror symmetry
We now want an image with periodic or quasiperiodic rotational symmetry that changes colors upon mirroring. Thus we need a colorchanging function U(x,y) that changes the sign U(x,y)=U(x,y) for its mirror image at the xaxis. We can easily get this … Continue reading