Tag Archives: Tessellation

Decorations of semi-regular tessellations

In the last posts I have shown kaleidoscopes that make repeating images in Euclidean, spherical and hyperbolic spaces. They are decorations of regular tilings. But what about semi-regular tilings? Could we decorate them too using mirrors? This would give us … Continue reading

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further wallpapers for hyperbolic space

An equilateral triangle gives us a kaleidoscope of three-fold rotational symmetry. With a square we get two-fold rotational symmetry. Would reflection at the sides of other regular polygons too give periodic images with rotational symmetry ? To get an h-fold … Continue reading

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irregular tilings and their duals

To get a better idea how the dualization method works we look at the same hexagonal tiling as before. Here is an image, where the triangles of the dual tiling are shaded: We now add a line to the original … Continue reading

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Tilings and their duals

I briefly discussed the dualization method in “The dualization method” but you will need more details to be able to understand my computer code. You can find some interesting ideas in Wolfram MathWorld and in Oracle ThinkQuest. In part I … Continue reading

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cellular automaton on the semiregular tesselation of squares and octagons

For a change I am looking again at cellular automatons. The results using a square lattice were not really satisfying, see “cellular automaton with color on a square lattice“. There, horizontal and vertical lines dominated too much. To get different … Continue reading

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Using the wrong harmonics …

If we combine sinusoidal waves making a square pattern, f(x,y)=cos(kx)+cos(ky) with other waves of higher frequency g(x,y)=cos(a kx)+cos(a ky) we should use an integer ratio a between the frequencies to get again the same periodicity. If the ratio a is … Continue reading

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Synthesizing quasiperiodic tilings

Synthesizers for electronic music combine simple waves to create complex sounds. Similarly, we create quasiperiodic structures from simple sinusoidal waves. I presented a first attempt in the post “quasiperiodic designs from superposition of waves“. A more complete method is discussed … Continue reading

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