Negative dimensions: Theory, computation, and experiment

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Abstract
Negative dimensions in probabilistic fractal measures are analyzed using the concept of level-independent multiplier distributions. By suitably manipulating these distributions we compute the positive and negative parts of the f(α) function. It is demonstrated that the multiplier method extracts the f(α) function with exponentially less work, and that it is more accurate than conventional box-counting methods. The utility of this method is demonstrated by applying it to a binary cascade with a triangular multiplier distribution and the dissipation field of fully developed turbulence.