Computer-Generated Art by using Fourier Series.
Fourier art is a form of computer art created by using Fourier series.
Fourier series are used to generate curves and surfaces, which are defined by parametric equations, expressing the coordinates of the points as different series.
For example, a two-dimensional parameterized curve is given by:
where a, b, c and d are Fourier coefficients.
By imposing simple algebraic conditions on Fourier coefficients, generated curves can present different kinds of symmetry and beautiful geometric properties, as shown in the images.
Fourier art also allows to generate animated images by smoothly varying the Fourier coefficients of a curve. This variation can be uniform for all coefficients or modeled with a specific function for each of them, which offers extensive possibilities for creating beautiful animations.
At this point, we are working on the development of an animated image generator for music visualization, varying Fourier coefficients according to changes in frequency and intensity of sound.