Expansion-Modification Systems: A Model for Spatial 1/f Spectra

Wentian Li

90-012

It is proposed in this paper that when two processes are competing with each other, one tends to create long-range correlations whereas another tends to destroy it, the limiting object consists of many length scales. In particular, it might have power-law correlation functions and spatial 1/f spectra. The basic features of this competing open dynamical process is captured by the model ‘expansion-modification system,’ first proposed in Ref. [24]. Many detailed properties of the system, both numerical and analytical, are discussed here. The implications of the proposed mechanism for power-law correlation functions to the evolution of galaxies and the evolution of nucleotide sequences are also discussed.