Applications of fractals in soil and tillage research: a review

Abstract Fractals are spatial and temporal model systems generated using iterative algorithms with simple scaling rules. This paper reviews the literature on spatial fractals as it applies to soil and tillage research. Applications of fractals in this area can be grouped into three broad categories: (i) description of soil physical properties; (ii) modeling soil physical processes; (iii) quantification of soil spatial variability. In terms of physical properties, fractals have been used to describe bulk density, pore-size distribution, pore surface area, particle-size distribution, aggregate-size distribution, ped shape and soil microtopography. In terms of physical processes, fractals have been used to model adsorption, diffusion, transport of water and solutes, brittle fracture and fragmentation. In terms of spatial variability, fractals have been applied to quantify distributions of soil properties and processes using semivariograms, power spectra and multifractal spectra. Further research is needed to investigate the specificity of different fractal models, to collect data for testing these models, and to move from the current descriptive paradigm towards a more predictive one. Fractal theory offers the possibility of quantifying and integrating information on soil biological, chemical and physical phenomena measured at different spatial scales.