1/f noise

Abstract

1/f noise is a nonstationary random process suitable for modeling evolutionary or developmental systems. It combines the strong influence of past events on the future and, hence somewhat predictable behavior, with the influence of random events. Nonstationary autocorrelation functions for 1/f noise are developed to demonstrate that its present behavior is equally correlated with both the recent and distant past. The minimum amount of memory for a system that exhibits 1/f noise is shown to be one state variable per decade of frequency. The system condenses its past history into the present values of its state variables, one of which represents an average over the most recent 1 unit of time, one for the last 10 time units, 100 units, 1000, 10000, and so on. Each such state variable has an equal influence on present behavior.