A row of cells, each on or off. The next row, drawn underneath, is worked out one cell at a time from that cell and its two neighbors: three cells have eight possible on/off patterns, and the rule says what each becomes. Eight yes/no answers make 256 possible rules, numbered 0 to 255 by reading the answers as a binary number. Type a rule number, pick a famous one, or click the buttons to build your own, and watch the rows pile up.

Stephen Wolfram studied these 256 rules in the 1980s and sorted their behavior into four classes: patterns that die out or freeze, simple repeating ones, chaos, and the rare edge-of-chaos rules whose structures interact. Rule 30 looks random even though it is completely deterministic from a single cell; rule 90 draws the Sierpinski triangle; rule 110 was proved capable of universal computation, so in principle it can run any program. The buttons above the picture are the rule itself: each column shows three cells and, below them, the cell they produce. Click a button to flip that answer and the rule number changes with it.

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