research on the evolution of the American urban system, for example, illustrates the evolutionary nature of human settlement systems. This research shows that early settlement patterns can create "path dependencies" for the future evolution of settlement systems. It also shows how economic restructuring, such as the shift from mercantilism to industrial capitalism, can create "bifurcation" of settlement systems with new nodes of growth in some regions and dissipation of growth in others (Borchert, 1967, 1987; Conzen, 1975; Dunn, 1980; Pred, 1981). Theoretical research has identified how the complexity of spatial economic dynamics reflects disequilibrating contradictions and social conflicts, resulting in periodic attempts by the private sector and the state to overcome emerging conflicts and crises through spatial restructuring (Harvey, 1982; Sheppard and Barnes, 1990).
Geographers have applied systems theory to help understand the complex interactions between nature and society that are caused by natural hazards, including multiple adjustments and attendant feedbacks (Cutter, 1993). Geographers have also examined the mechanisms of ecosystem stability and change, especially human and other agents of short-and long-term ecosystem change (Zimmerer, 1994). Ideas about chaotic behavior or catastrophic events within places, additionally, have contributed to research on growth within and among cities (Allen and Sanglier, 1979; Dendrinos, 1992). These studies illustrate geographers' contributions to a more fundamental understanding of environmental and social systems in ways that should engage ecologists, engineers, mathematicians, physicists, and other members of the scientific community.
Other geographic research has been directed toward the identification and description of patterns that may have emerged from nonlinear, complex, or chaotic dynamics. Fractal dimensions, in particular, have been used to simplify and represent the outcomes of nonlinear, chaotic, or complex dynamics (Goodchild and Mark, 1987). Urban settings (Batty and Longley, 1994) as well as satellite and map images (Malanson et al., 1990) have been usefully analyzed and characterized with fractals.
Interactions in space and with nature tend to result in certain spatial and environmental regularities, leading to the study of expected outcomes, or central tendencies, across geography's domains of interest (Chorley and Haggett, 1967). Geographers have recognized, however, that observable geometries in the social and physical worlds are dynamic in their nature and multidimensional in their explanation. Certain geographic patterns reflect efficiency (as in economic production systems), but only under rather narrowly defined conditions that are subject to change (such as the time or cost of travel) and to inherent variability. Together, change and inherent variability often influence the observed variation, which can take the form of unsystematic departures from central tendency, changes to the central tendency itself, or alterations in the variance structure. Changes in variation can signal shifts from one system state to another; therefore, variation cannot be