Spatial 1/ f Spectra in Open Dynamical Systems
Wentian Li · Europhysics Letters (EPL) · 1989
A new mechanism for spatial 1/ f power spectra is proposed for a type of open dynamical system. This mechanism has two competing ingredients. One tends to preserve the long-range correlations while the other tends to destroy it. A specific model with this mechanism based on a class of extremely simple context-free grammars is analyzed. In this model replication and transposition are repeated applied to a string of discrete elements. Computer experiments show that for a wide range of parameter values, the model yields spatial power spectra of the form 1/ f α with α close to 1. The frequency range spanned by the 1/ f α form as well as the exponent α depend on the probability with which replication and transposition operations are applied.