Abstract
This paper considers the propagation of a pulse through a theoretical fractal network. Thd multi-fractal characteristics and spectral features resulting from the decorrelation of a pulse as it transits the network, are discussed. Analogies to naturally occuring networks, such as the His-Purkinje system of the myocardium, are considered. The fractal dimension ( D F), multi-fractal (f(α)) spectrum and the power spectrum [ V(ω)] reflect the oganizational features of the network. D F and f(α) are global measures that describe the geometric structure based on segment length, generation, and scaling factors. V(ω) measures the heterogeneity of the pathways present in the network which, in turn, reflects the distribution of the segment length variations throughout the network. Multi-fractal analysis and the spectral features of the decorrelation distribution provide additional information regarding the structural organization of fractal networks relevant to understanding the role of critical dimensions or scales within a complex fractal structure whether related to propagation features, vibrational modes or heterogeneity considerations.
Published Version
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