Colored noise generation through deterministic chaos

The apparently stochastic properties of deterministic-chaotic sequences generated by hierarchies of nonlinear recursive loops are illustrated, as is the capability of such sequences to exhibit seemingly arbitrary spectral coloring. An approximate, though usefully accurate, approach to estimating probability density functions of sequences is developed The synthesis of sequences having prescribed statistics is examined. The tendency of power spectra of sequences to exhibit an increasingly excess low-frequency character as the number of loops in a hierarchy increases is illustrated. New insights are presented into (a) the generation of 1/f noise and (b) whether any species of noise need have a random origin.>