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Proteins have been shown to exhibit strange/anomalous dynamics displaying non-Debye density of vibrational states, anomalous spread of vibrational energy, large conformational changes, nonexponential decay of correlations, and nonexponential unfolding times. The anomalous behavior may, in principle, stem from various factors affecting the energy landscape under which a protein vibrates. Investigating the origins of such unconventional dynamics, we focus on the structure-dynamics interplay and introduce a stochastic approach to the vibrational dynamics of proteins. We use diffusion, a method sensitive to the structural features of the protein fold and them alone, in order to probe protein structure. Conducting a large-scale study of diffusion on over 500 Protein Data Bank structures we find it to be anomalous, an indication of a fractal-like structure. Taking advantage of known and newly derived relations …