Expansion-modification systems: A model for spatial 1/f spectra.

It is proposed in this paper that when two processes competing with each other, one tends to create long-range correlations whereas another tends to destroy it, the limiting object consists 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 expansionmodification system, first proposed in Ref.[24]. Many detailed properties of the system, both numerical and analytical, are discussed here. The implication of the proposed mechanism for power-law correlation functions to the evolution of galaxies and the evolution of nucleotide sequences are also discussed.