
Recent Posts
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
 Apollonian gasket as a spherical fractal with tetrahedral symmetry
 waves – a browser app for creating quasiperiodic wallpapers
Recent Comments
Archives
 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
Monthly Archives: November 2012
Ornaments of fourfold rotational symmetry
As mentioned in “The benefit of programming mistakes” I am trying to simulate the growth of snow crystals using a modified cellular automaton. Cellular automatons are used in Conway’s game of life and as morphological filters in digital image processing. But … Continue reading
Posted in Cellular automata
Tagged generative design, ornament, Rotational symmetry, Selfsimilarity
Leave a comment
Color symmetry from more than two waves
In the last post we got a hue from two wave functions resulting in twocolor symmetries. The method can be extended to any number n of wave functions f_i(x,y). Just think of n points distributed evenly on the unit circle … Continue reading
Posted in Quasiperiodic design
Tagged color symmetry, Quasiperiodic design, Rotational symmetry
Leave a comment
color symmetry from two wave functions
Hue is a cyclic variable going from red to yellow, green, cyan, blue, magenta and then back to red again. Thus it behaves like an angle. Using full saturation and brightness we then calculate such a spacedependent angle or hue … Continue reading
Posted in Quasiperiodic design
Tagged color symmetry, Quasiperiodic design, Rotational symmetry
Leave a comment
Another way to see designs from waves with 12fold rotational symmetry
In the last post I have shown the superposition of two wave patterns with hexagonal symmetry. This yields designs with 12fold rotational symmetry related to the Stampfli tiling. Now, similarly as in “Quasiperiodic designs from waves and higher dimensional space” we … Continue reading
Posted in Quasiperiodic design
Tagged Quasiperiodic design, quasiperiodic Tiling, Stampfli tiling
Leave a comment
Stampflitiling and related designs from waves
Three sinusoidal waves make a hexagonal pattern for f(x,y)=cos(x)+cos(x/2+sqrt(3) y/2)+ cos(x/2+sqrt(3) y/2), see the figure at left. Using this and the same pattern rotated by 90 degrees we get patterns of 12fold rotational symmetry. I found it interesting to draw … Continue reading
From twocolor to single color tenfold rotational symmetry
In “Quasiperiodic designs from superposition of waves” I showed two different designs with tenfold rotational symmetry, one with a twocolor symmetry and another with a single color symmetry. In spite of this great difference they are actually crosssections of the … Continue reading
The benefit of programming mistakes
I wanted to simulate the growth of snow crystals using a modified cellular automaton. A wellknown cellular automaton is Conway’s game of life. This should give me some fractal structures of hexagonal symmetry. However, due to false reasoning or programming mistakes … Continue reading