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 mirror-symmetry 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

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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 left-overs. It is not possible to find an iteration method for the Stampfli tiling. One finds easily how to … Continue reading

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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

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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

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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

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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

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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:

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