Spatial representation of symbolic sequences through iterative function systems

Jeerey 10] proposed a graphic representation of DNA sequences using Barns-ley's iterative function systems. In spite of further developments in this direction 19, 25, 13], 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 Jeerey's graphic representation to accommodate (possibly innnite) sequences over an arbitrary nite number of symbols, 2) establish a direct correspondence between the statistical characterization of symbolic sequences via R enyi entropy spectra and the multifractal characteristics (R enyi generalized dimensions) of the sequences' spatial representations, 3) show that for general symbolic dynamical systems, the multifractal f H-spectra in the sequence space coincide with the f H-spectra on spatial sequence representations.