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To characterize fractals, a function is introduced which is a natural extension of the fractal dimension. This fractal dimension function is easily evaluated numerically and is amenable to a theoretical description. In particular, an intimate connection between fractal dimension and statistics is uncovered. As illustrative examples the concept is applied to sequences of random numbers and to the energy levels of coupled harmonic oscillators.
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Cederbaum et al. (1985) studied this question.
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