The basic theory is pretty simple. Color fading happens as the dyes in the print degrade, which happens at different rates for the three different dyes (cyan, magenta, and yellow). The color distributions shift to brighter intensities. The distribution of the concentration of dyes is logarithmically related to the color intensity distributions of red, green, and blue. Over a large enough number of pixels/frames the average color is gray, which follows from the central limit theorem, and voila, you’ve got an algorithm.