Modeling geocomplexity: “A new kind of science”

A major objective of science is to provide a fundamental understanding of natural phenomena. In “the old kind of science” this was done primarily by using partial differential equations. Boundary and initial value conditions were specified and solutions were obtained either analytically or numerically. However, many phenomena in geology are complex and statistical in nature and thus require alternative approaches. But the observed statistical distributions often are not Gaussian (normal) or log-normal, instead they are power-laws. A power-law (fractal) distribution is a direct consequence of scale invariance, but it is now recognized to also be associated with self-organized complexity. Relatively simple cellular-automata (CA) models provide explanations for a range of complex geological observations. The “sand-pile” model of Bak — the context for “selforganized criticality” (SOC) — has been applied to landslides and turbidite deposits. The “forest-fire” model provides an explanation for the frequency-magnitude statistics of actual forest and wild fires. The slider-block model reproduces the Guttenberg-Richter frequency-magnitude scaling for earthquakes. Many of the patterns generated by the CA