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 lognormal, 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 “self-organized criticality”—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 approach can be recognized in geological contexts. The use of CA models to provide an understanding of a wide range of natural phenomena has been popularized in Stephen Wolfram's bestselling book A New Kind of Science (2002). Since CA models are basically computer games, they are accepted enthusiastically by many students who find other approaches to the quantification of geological problems both difficult and boring.