ABSTRACT
This chapter focuses on applying percolation theory to soil formation, vegetation growth, natural and intensively managed, and net primary productivity. The description of these paths may be dominated by characteristics of the medium, but the paths tend to conform to the fractal geometry of percolation. Fractal exponents of percolation theory, which describe such quantities as the backbone of the percolation cluster, tortuosity of optimal flow paths, and the mass of randomly connected objects, are relevant in the biogeosciences. The fundamental conclusions of percolation theory are strongly dependent on the dimensionality of the system. Large clusters near the percolation threshold are characterized by large holes, loops and many dead ends, which can be composed of interconnections of bonds, but which connect to the remainder of the cluster only at one point. The chapter addresses the fractal topology of the flow paths, where the scaling arguments of percolation theory enter.
