Real time pink noise generation with rain visualization.
The Voss-McCartney algorithm is used to generate the pink noise. The algorithm essentially involves having multiple white noise generators that each update at different rates, as detailed in the gif below. These noise generators are summed every iteration to produce the next sample. I've found that 15 generators (plus a continually updating white noise generator) produces a pleasant sounding pink noise.
Included in this repository is a model of the algorithm, which shows that if you average several runs of the algorithm you get a pretty close to ideal pink noise frequency response. Pink noise is characterised by it's 1/f frequency response as detailed in the diagram below. There are some noticible ripples there but it is insignificant to the human ear :).