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Tag Archives: Tessellation
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
Posted in Quasiperiodic design, Tilings
Tagged dual tesselation, quasiperiodic Tiling, Tessellation
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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
Posted in Tilings
Tagged dual, dual tesselation, dualization, network, Tessellation, Tiling
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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
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
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
Morphing the tiling of octagons and squares
In the last post “Doubling the tessellation of octagons and squares” I have used a grid of squares (in black) with diagonals (in blue). The blue lines are distinct and cannot be mapped onto the black lines by the symmetries … Continue reading
Posted in Tilings
Tagged Ammannâ€“Beenker tiling, Art, quasiperiodic Tiling, Rotational symmetry, Tessellation
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Doubling the tessellation of octagons and squares
Regular octagons and squares make up a wellknown semiregular tessellation that is often used to decorate floors Its dual grid is essentially a square grid with diagonal lines added. Four lines cross at the corner points giving the octagons of … Continue reading
Posted in Tilings
Tagged Ammannâ€“Beenker tiling, Art, Geometry, quasiperiodic Tiling, Rotational symmetry, Tessellation
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