Symbolic strings and spatial 1/f spectra

Some string dynamics which are expected to show non-trivial correlations ar e proposed and studied. It is because we were motivated by the observation that some DNA sequences show spatial 1/f correlation. Our model is based on a rule by which one string is split into two parts in the middle and anoth er string is inserted between them when the strings are made longer. The ba sic model shows long-range correlations with a structure characteristic of cyclic patterns on the log-log plot of the spectrum. The effects of string cross-over and point-mutation are also studied. The cross-over destroys the structures appearing in the basic model and makes 1/f-like correlation cle ar. The point-mutation makes the power spectrum flat as is expected from th e white-noise nature. The analogy of the cross-over model with real DNA evo lution dynamics is suggested. (C) 1999 Elsevier Science B.V. All rights res erved.