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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: interference pattern
7 and 14fold rotational symmetry from waves
Similarly as for 5 and 10fold rotational symmetry, see “quasiperiodic design with fivefold rotational symmetry …“, we can create designs with 7 and 14fold rotational symmetry. Here are some examples: In comparison we get here larger round, mandalalike motivs around … Continue reading
Another design with tenfold rotational symmetry from waves
For tenfold 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 getÂ depends strongly on the choice … 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
Quasiperiodic pattern from eight waves and the AmmannBeenker tiling
Using four waves at right angles we get a periodic structure of fourfold symmetry. A square grid of the same periodicity is easily fitted to this structure. Now, together with an extra set of four waves rotated by 45 degrees … Continue reading