Monthly Archives: November 2012

Ornaments of four-fold 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

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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 two-color 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

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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 space-dependent angle or hue … Continue reading

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Another way to see designs from waves with 12-fold rotational symmetry

In the last post I have shown the superposition of two wave patterns with hexagonal symmetry. This yields designs with 12-fold rotational symmetry related to the Stampfli tiling. Now, similarly as in “Quasiperiodic designs from waves and higher dimensional space” we … Continue reading

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Stampfli-tiling 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 12-fold rotational symmetry. I found it interesting to draw … Continue reading

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From two-color to single color ten-fold rotational symmetry

In “Quasiperiodic designs from superposition of waves” I showed two different designs with ten-fold rotational symmetry, one with a two-color symmetry and another with a single color symmetry. In spite of this great difference they are actually cross-sections of the … Continue reading

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The benefit of programming mistakes

I wanted to simulate the growth of snow crystals using a modified cellular automaton. A well-known 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

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