# 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 bulls-eyes. Here I want to show similar results … Continue reading

## Another design with ten-fold rotational symmetry from waves

For ten-fold 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