Negative dimensions: Theory, computation, and experiment
Abstract
Negative dimensions in probabilistic fractal measures are analyzed using the concept of levelindependent 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 boxcounting 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.
 Publication:

Physical Review A
 Pub Date:
 January 1991
 DOI:
 10.1103/PhysRevA.43.1114
 Bibcode:
 1991PhRvA..43.1114C
 Keywords:

 05.45.+b;
 02.50.+s;
 03.40.Gc;
 47.25.c