Dynamic Epicycles
Behind many modern technologies in fields like spectral analysis and data compression is a piece of math called the Fourier transform.
Because the transformation allows us to compute Fourier coefficients given an absolutely integrable function we can decompose curves in the complex plane into a combination of added rotating vectors called dynamic epicycles. We can use this to redraw curves using their corresponding Fourier Series. Arbitrary images are not usually given as mathematical functions however, so we must instead use the Discrete Fourier Transform (DFT) on a sampling of points when using images in jpg or png file formats.
