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 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
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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
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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
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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
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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
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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