Multifractal modeling and lacunarity analysis

The so-called ''gliding box method'' of lacunarity analysis has been investigated for implementing multifractal modeling in comparison with the ordinary box-counting method. Newly derived results show that the lacunarity index is associated with the dimension (codimension) of fractal, multifractal and some types of nonfractals in power-law relations involving box sire; the exponent of the lacunarity function corresponds to the fractal codimension (E - D) for fractals and nonfractals, and to the correlation codimension (E - tau(2)) for multifractals. These results are illustrated with two case studies: De Wijs's zinc concentration values from the Pulacayo sphalerite-quartz vein in Bolivia and Cochran's tree seedlings example. Both yield low lacunarities and slightly depart from translational invariance.