The beginnings of fractals can be traced to hydrologic studies, dating back to the late 1960s with Mandelbrot's description of river flow as a self-similar process. Early applications of fractal concepts included the description of the length of coastlines and fracture patterns in the spatial domain, and river discharge in the temporal domain. Recent efforts to apply fractal concepts to hydrologic phenomena have produced new organizing principles for understanding the life cycle of water on Earth as it affects the terrestrial landscape and subterranean geologic deposits.
Fractal mathematics offers a natural way to describe irregular patterns if they contain fine structure that is encountered repeatedly over a range of spatial or temporal scales [Meakin, 1991]. Like the objects of classical geometry—circles and spheres—the objects of fractal geometry are idealizations that are only approximated in natural systems, but are nonetheless useful for mathematical description [Guyon and Stanley, 1991].