
Recent Posts
 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
Recent Comments
Archives
 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: programming
Rotational symmetry from space with an odd number of dimensions
We now look at the easier case for the post “Quasiperiodic and periodic kaleidoscope from higher dimensional space“, where the embedding space has an odd number of dimensions, p=2q+1. The unit vectors lie at equal angles and form a star … Continue reading
Posted in Kaleidoscopes, programming, Quasiperiodic design
Tagged Rotational symmetry
Leave a comment
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
Changing the hue
It has been easy to find special color transformations for 2 and 3color symmetries. For other color symmetries I use a rather general color transformation that changes the hue. First, we separate the pixel color in a grey part and … Continue reading
Posted in Kaleidoscopes, programming
Tagged Color, color manipulation, hue, programming
Leave a comment
Color transformation
I am now discussing color transformations for creating kaleidoscopic images with twocolor symmetry. Each pixel has three color components: red, green and blue. Their values are between 0 and 255. Thus we can think that a pixel color is a point with … Continue reading
Posted in Kaleidoscopes, programming
Tagged Colors, false colors, negative image, transformation, twocolor symmetry
Leave a comment
Kaleidoscopes with twofold color symmetry.
A checkerboard is a square lattice with twofold color symmetry. The alternating black and white squares make it more interesting than a simple square lattice. Thus I want to have too some twofold color symmetry for our kaleidoscopes. Farris has done this … Continue reading
Posted in Kaleidoscopes, programming
Tagged color symmetry, kaleidoscope, programming, twocolor symmetry
Leave a comment
How to generate rosettes
A rosette is an image with rotational symmetry. For pfold symmetry we can use the methods of the last post “Anamorphosis and symmetries” with a simple power as a mapping function between output and input images: Here z=x+iy relates to … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged anamorphosis, image processing, programming, Rotational symmetry
Leave a comment
Anamorphosis and symmetries
As proposed by Farris in “Creating Symmetry” we can use anamorphosis to make images of any symmetry from some other input image. Here I briefly discuss how I am doing it and what you will find in my next program. Each … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged kaleidoscope, programming, symmetry
Leave a comment