Probabilistic Multifractals and Negative Dimensions
We propose that negative dimensions can be best understood using the concept of level-independent multiplier distributions and show that, by utilising them, one can extract the positive and negative parts of the f(α) function with exponentially less work than by using conventional boxcounting methods. When the underlying multiplicative structure is not known, both methods of computing negative dimensions can give spurious results at finite resolution. Applications to fully developed turbulence are discussed briefly.
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