Mathematical Geology

, Volume 29, Issue 7, pp 919–932

Multifractal Modeling and Lacunarity Analysis


  • Qiuming Cheng
    • Department of Earth and Atmospheric Science, Department of GeographyYork University

DOI: 10.1023/A:1022355723781

Cite this article as:
Cheng, Q. Mathematical Geology (1997) 29: 919. doi:10.1023/A:1022355723781


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 – τlpar;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.

multifractalsfractallacunaritygliding boxbox-countingmoments
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© International Association for Mathematical Geology 1997