Spatial-Domain Chaos in Landscapes

It has been speculated that deterministic chaos may be responsible for the spatial complexity commonly observed in biophysical landscapes. However, deterministic chaos is a temporally defined concept and has been rigorously investigated only in the temporal domain. It is shown here, using a simple hillslope regolith cover model as an example, that temporal chaos in the presence of even minor spatial anisotropy will result in a spatially chaotic pattern. It is also shown that behavior of spatially chaotic landscape systems can be deduced, at least in theory, from spatial patterns of a single landscape component or variable. Because stochastic complexity is likely to exist in landscapes in addition to any deterministic complexity, detecting and analyzing chaotic behavior in landscapes is difficult. Progress in efforts to examine chaos in the spatial domain and to isolate deterministic and stochastic complexity may be the key to developing a theory of landscape evolution that can reconcile the simultaneous presence of apparently random, irregular variability and orderly, regular patterns.