
Recent Posts
Recent Comments
Archives
 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
Tag Archives: mirror symmetry
The rotational and mirror symmetry at the center
In the last post I used mirror symmetry at two crossing straight lines and the related inversion at a circle. The mirror symmetries generate a krotational symmetry for an angle of intersection of π/k. With these symmetries I map any point … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, mirror symmetry, rosette, Rotational symmetry
Leave a comment
A hyperbolic kaleidoscope
In “creating symmetry” Frank Farris shows a wallpaper for hyperbolic space. He uses the Poincaré plane to project the hyperbolic space to our Euclidean drawing surface. The wallpaper then results from mirror symmetries at vertical lines at x=0 and x=0.5 … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged hyperbolic space, inversive geometry, kaleidoscope, mirror symmetry, Poincaré plane
Leave a comment
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
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
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
Mirror symmetry and rotational symmetry
To study mirror symmetry at the xaxis together with rotational symmetry we can do similarly as in the earlier post “improved symmetric sum“. Here I prefer to present only the conclusions, which you could get by intuition too. It is important … Continue reading
Rotations, mirrorsymmetry and the scalar product
In the last post we have seen that scalar products between a pixel’s position in the output image and certain vectors e define periodic and quasiperiodic designs. We want symmetric images and thus we have to see how the scalar product changes … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming, Tilings
Tagged Math, mirror symmetry, Rotational symmetry
Leave a comment