Creating Digital Art Using 2D Fourier Transforms Creating Digital Art Using 2D Fourier Transforms By Gustaf Ullman Introduction Digital art can explore concepts and techniques rooted in mathematics. One such method involves the use of two-dimensional Fourier transforms to create intricate and randomized patterns. This article outlines how to generate "lumpy" images in CMY (cyan, magenta, yellow) using a simple spectral construction. Method The process begins by specifying a radially symmetric amplitude profile in the spatial-frequency domain , for example: f(r) = A exp(-br) where r is the radial frequency (distance from the center in the Fourier plane), A is an amplitude scale, and b controls how quickly the spectrum decays with frequency. Next, assign a random phase to each Fourier coefficient, sampled uniformly in [0, 2π) , and form a complex spectrum F(k) = f(|k|) · exp(iφ(k)) where...
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