Spatial representation of symbolic sequences through iterative function systems

Authors:
P. Tino
Affiliations:
Austrian Res. Inst. for Artificial Intelligence, Vienna
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Year:
1999

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Abstract

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 fH-spectra in the sequence space coincide with the fH -spectra on spatial sequence representations