Natural and Fractal Fluctuations in Time, Noise, and Music

Abstract

Noise is an unpredictable variation of some variable in time. White noise is a completely random variation in time. This means that for short or long time intervals there is no correlation between one segment of the variation and any other. If one integrates this random or white noise, the result is brown noise. Brown noise has a fairly strong statistical correlation between different segments of the variation. Brown noise has more low frequency than high frequency fluctuations. It receives its name because it is a good model of Brownian motion (Barnsley et al., 1988). Brownian motion is the term given to the random motion of a very fine particle suspended in a liquid. The thermal motion of the molecules of the liquid push the particle around in a random fashion. The position of the particle in the fluid is highly correlated to previous positions of the particle.