The most common power law is the Pareto distribution, named for the 19th-century Italian economist Vilfredo Pareto. In the late 1890s, Pareto argued that in any given society, 20 percent of the people will hold 80 percent of the wealth. But the Pareto distribution, also known as the “80-20 rule,” holds in such diverse human contexts as size of settlements (a few big cities, many smaller towns) and frequency of words in text (a few words used often, most words infrequently), as well as for natural phenomena like the size of sand particles and of meteorites. That the behavior of Sugarscape’s automata yielded power law-type distributions indicated to Epstein and Axtell that they were on to something.
In the early 1990s, Epstein gave a presentation at the Santa Fe Institute in New Mexico, a center for the study of complex adaptive systems across natural, human, and artificial contexts. “I showed one of our artificial histories set in the standard Sugarscape landscape with two sugar peaks, a sugar lowland in the middle, and sugar badlands on the sides–effectively, a simple valley representation,” Epstein told me. “I asked the audience if it reminded anybody of anything. George Gumerman’s hand shot up, and he said, ‘It reminds me of the Anasazi.’”
George Gumerman is an anthropologist who for decades has been a leading expert on the Anasazi, ancestors of the present-day Pueblo peoples who from roughly 1800 b.c.e. to 1300 c.e. inhabited Long House Valley in northeast Arizona. Epstein and Axtell decided to use their agent-based modeling to create a virtual Anasazi civilization and see how it matched up against the extensive database of settlement patterns and the like assembled by Gumerman and his colleagues. Epstein recalled, “We started over, building the artificial terrain from scratch, with great exactitude.” Elements like climate patterns, maize yields, fluctuations of the water table, and multitudes of other factors went into the model. “The big trick was, Could we come up with good rules for our artificial Anasazi, put them where the real ones were in 900 a.d., and let them run till they grew the true history?” Epstein remembered one session in which his team’s artificial Anasazi established a settlement exactly where Long House, the real Anasazi settlement, had been. “We just sat screaming into the air with gratification. The entire business has come an awfully long way since then. Now there’s many people doing this kind of work.”
Indeed. The website of the Journal of Artificial Societies and Social Simulation, for instance, lists papers with titles such as “Cascades of Failure and Extinction in Evolving Complex Systems.” Epstein’s new book collects his own papers since 1996; an accompanying CD lets readers watch runs of the models described in the text and explore the models on their own. In the projects described in the book, Epstein and his collaborators modeled, in addition to the Anasazi, the emergence of various phenomena: patterns in the timing of retirement; social classes; thoughtless conformity to social norms; patterns of smallpox infection after a bioterrorist incident; and successful, adaptive organization.