Brownian noise ls known as Brown noise or red noise, is the kind of signal noise produced by Brownian motion hence its alternative name of random walk noise. The term "Brown noise" comes not from the color, but after Robert Brown, the discoverer of Brownian motion.
The graphic representation of the sound signal mimics a Brownian pattern. Its spectral density is inversely proportional to f², meaning it has more energy at lower frequencies, even more so than pink noise. It decreases in power by 6 dB per octave and, when heard, has a "damped" or "soft" quality compared to white and pink noise. The sound is a low roar resembling a waterfall or heavy rainfall. See also Purple noise, which is a 6 dB increase per octave.
Brown noise can be produced by integrating white noise. That is, whereas (digital) white noise can be produced by randomly choosing each sample independently, Brown noise can be produced by adding a random offset to each sample to obtain the next one.