Monthly Archives: October 2012

Periodic and quasiperiodic images from cross-sections of 4-dimensional space

In the earlier post “Quasiperiodic designs from waves and higher dimensional space” I have shown that the quasiperiodic wave pattern with 8-fold rotational symmetry is a special cross-section of a periodic pattern in  4-dimensional space. Here I will rotate the … Continue reading

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Design from waves with ten-fold rotational symmetry using another color model

Instead of controlling directly the color components red, green and blue with the waves we can use the hue-saturation-brightness color model. In this example the waves of lowest frequency change the brightness. Waves of higher frequency change the hue. Saturation … Continue reading

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7- and 14-fold rotational symmetry from waves

Similarly as for 5 and 10-fold rotational symmetry, see “quasiperiodic design with five-fold rotational symmetry …“, we can create designs with 7 and 14-fold rotational symmetry. Here are some examples: In comparison we get here larger round, mandala-like motivs around … Continue reading

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Another design with ten-fold rotational symmetry from waves

For ten-fold rotational symmetry it is quite natural to begin with ten rhombs and angles of 36 degrees. This gives a larger rosette of rhombs than in the post before. The quasiperiodic design I get  depends strongly on the choice … Continue reading

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Quasiperiodic design with five-fold rotational symmetry in color

An easy way to get color is using three different sets of waves to control the three basic colors red, green and blue. The green color is the brightest one and thus used for the waves of lowest frequencies. The … Continue reading

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Quasiperiodic designs from waves and higher dimensional space

I am doing it again – a rather mathematical post. Well, in “An easy way to quasiperiodic tilings” I have shown how to make the Ammann-Beenker tiling using two square grids. Then in “How to find these corner points of … Continue reading

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A tiling with squares and triangles only

One can go to the other extreme and find suitable dissections of the square and the equilateral triangle without rhombs. For the square we get two different compositions of the sides. Thus we need two different kinds of triangles to … Continue reading

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