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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Monthly Archives: September 2012
A tiling with triangles and rhombs only
We can dissect the rhomb into triangles and rhombs without using squares. This dissection destroys its mirrorsymmetry but leaves the rotational symmetry around its center intact. Together with the dissection of the triangle into rhombs and triangles shown in the … Continue reading
Posted in Tilings
Tagged enantiomorphic, Iterative method, mirror symmetry, quasiperiodic Tiling, Rotational symmetry
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Finding an iteration method for the Stampfli tiling – mission impossible
I have caught a cold. I am not able to do new work and thus I am writing up some old leftovers. It is not possible to find an iteration method for the Stampfli tiling. One finds easily how to … Continue reading
Posted in Tilings
Tagged iteration, Iterative method, quasiperiodic Tiling, Stampfli tiling
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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
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
Autumn leaves
In autumn find a lot of colorful leaves and we dry them. Later we are disappointed as they lose their color and become brittle. Thus I now prefer to scan the leaves with the scanner on my printer. It is … Continue reading
Making quasiperiodic structures using waves: A simple program
// this is a simple program // it shows more clearly how I get quasiperiodic structures // from waves // feel free to experiment //———————————————— // to run the program you need processing // simply download processing from processing.org … Continue reading
Experiments with waves
I extended the program that mixes waves to get some more decorative and less scientific pictures. Using n=9 and a nonlinear color model gives: