In this paper, we present the results of a heavy metal soil geochemical survey in Hefei city and use three multifractal parameters to indicate the overall amount of multifractality within the soil geochemical data. The results show all of the elements barring Hg have larger multifractal parameters in the Daxing area compared to the Yicheng area. The degree of multifractality suggests that the differing economic activities in Daxing and Yicheng generate very different heavy metal pollution loads.

Percolation theory can be used to find flow paths of least resistance. Applying percolation theory to drainage networks apparently allows identification of the range of exponent values describing the tortuosity of rivers in real networks, thus generating observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on assessment of substrate heterogeneity.

In the present study, we investigate the scaling properties of the topography of Mars. Planetary topographic fields are well known to exhibit (mono)fractal behavior. Indeed, fractal formalism is efficient in reproducing the variability observed in topography. Our results suggest a multifractal behavior from the planetary scale down to 10 km. From 10 km to 300 m, the topography seems to be simple monofractal.

In order to refine our understanding of how fluid inclusions were trapped in the host minerals, we observed mercury inclusions in quartz samples using X-ray computed tomography technique. We obtained three-dimensional spatial distributions, and analyzed them using fractal and multifractal methods. Given the fractal dimension and its implied mechanism, the mercury-bearing fluids were not primary fluid inclusions, but migrated into the pre-existing cracks of quartz crystals by diffusion processes.