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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: Fourier series
Five fold rotational symmetry: Tuning the harmonics
In “better images from higher harmonicsĀ ?” I have replaced the basic sine and cosine functions by Fourier series approaching a symmetric triangular wave. This gave images with more details and somewhat smaller bullseyes. Here I want to show similar results … 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 getĀ 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
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