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 size; the exponent of the lacunarity function corresponds to the fractal codimension (E - D) for fractals and nonfractals, and to the correlation codimension (E - τ(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.
CITATION STYLE
Cheng, Q. (1997). Multifractal Modeling and Lacunarity Analysis. Mathematical Geology, 29(7), 919–932. https://doi.org/10.1023/A:1022355723781
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