Negative dimensions: Theory, computation, and experiment

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.