Generating 1/fβ noise with a low-dimensional attractor characteristic: its significance for atomic vibrations in proteins and cognitive data

We propose an iterative correlator with random seeds as a method to generate series characterized by a low-dimensional attractor (D≈4.65) and scaling properties described by a power law P=1/fa where 0<a<≈2. The method basically introduces an interaction factor between the terms of the series. The higher the interaction factor the stronger the correlation. The attractor properties disappear at interaction factors generating scaling exponents lower than about a=0.25. The method proved to be useful for describing the nonlinear properties of the atomic vibrations in the main chain of proteins as well as series of data produced in cognitive experiments.