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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
 Fractal tiling of a sphere with octahedral twocolour symmetry
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Tag Archives: Tessellation
Decorations of semiregular 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 semiregular tilings? Could we decorate them too using mirrors? This would give us … Continue reading
Posted in Kaleidoscopes, Tilings
Tagged hexagonal lattice, kaleidoscope, mirror symmetry, Tessellation
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further wallpapers for hyperbolic space
An equilateral triangle gives us a kaleidoscope of threefold rotational symmetry. With a square we get twofold rotational symmetry. Would reflection at the sides of other regular polygons too give periodic images with rotational symmetry ? To get an hfold … Continue reading
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