Wired 10.06: Rule 30

The Wolfram worldview focuses on simple rules that generate counterintuitively complex results, observable in computer-based systems called cellular automata. A two-dimensional CA "grows" one line at a time, and each new cell's state - light or dark - is determined by the cells on the previous line. Three-cell configurations produce eight possible combinations (see top line); Wolfram studied all the rules that result. The experiment illustrated here, using his Rule 30, begins with a single dark cell in the middle of a line. With each line, the rule creates new patterns. The left side seems to grow in a fairly orderly fashion, but the right side is unpredictable. One might expect that a simple rule would lead to a consistent order in the entire output, but the eventual result is still fantastically complex (right). After 20 years of study, Wolfram concluded that the Rule 30 phenomenon - a simple rule generating deep complexity - is widespread in the natural world.