Stephen Wolfram’s book “A New Kind of Science” has become a best seller. The theme of the book is that problems in complexity are best approached using “cellular automata” (CA). The cornerstone of complexity studies were laid in the geological sciences in general, and in geology in particular. Examples include the Horton-Strahler classification of drainage networks. Mandelbrot’s length of a rocky coastline (the context for the introduction of the term “fractals”), and the Guttenberg-Richter frequency-magnitude relation for earthquakes. A number of CA models have been introduced in terms of geological applications. The “sandpile” model of Bak (the context for “self-organized criticality”) was applied to landslides and turbidite deposits. The “slider-block” model provides an explanation for the frequency-magnitude statistics of earthquakes. A simple CA model provides a general explanation for the evolution of landforms. Randomly dropped “particles” are allowed to migrate to adjacent grid sites following simple rules. The Brownian-walk statistics of topography are reproduced. A simple variation on this model also reproduces the structure and migration of coastlines (beaches). The CA approach generates a wide range of patterns, many of these patterns can be recognized in geological contexts. The CA approaches do not entirely replace the classical use of differential equations, tensors, etc. However, the attractiveness of the computer-based CA approach to many students who take offense at equations is evidence that the approach could play an important role in undergraduate geology courses.