Spatial representation of symbolic sequences through iterative function systems

Jeffrey proposed (1990) a graphic representation of DNA sequences using Barnsley´s iterative function systems. In spite of further developments in this direction, the proposed graphic representation of DNA sequences has been lacking a rigorous connection between its spatial scaling characteristics and the statistical characteristics of the DNA sequences themselves. We 1) generalize Jeffrey´s graphic representation to accommodate (possibly infinite) sequences over an arbitrary finite number of symbols; 2) establish a direct correspondence between the statistical characterization of symbolic sequences via Renyi entropy spectra (1959) and the multifractal characteristics (Renyi generalized dimensions) of the sequences´ spatial representations; 3) show that for general symbolic dynamical systems, the multifractal f/sub H/-spectra in the sequence space coincide with the f/sub H/-spectra on spatial sequence representations.