This chapter shows how complex shapes and forms encountered in the natural world result from a growth process driven by the repeated action of simple “rules.” To examine this general idea, the chapter focuses on cellular automata, arguably the simplest type of computer programs conceivable yet can sometimes exhibit behaviors that are extremely complex. Cellular automata are also a classic example of simple rules being able to produce complex global “patterns” that cannot be inferred or predicted even if we have complete, a priori knowledge of these rules. The chapter first considers cellular automata in one and two spatial dimensions before discussing a zoo of two-dimensional structures from simple rules. It then describes the role of agents in iterated growth as well as emergent structures and behaviors that can be produced by cellular automata. The chapter includes exercises and further computational explorations, along with suggested materials for further reading.
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