An elementary cellular automaton is a single row of cells. Each new row is computed from the one above: a cell looks at itself and its two neighbours (3 bits, 8 possibilities) and a lookup table says whether it's on. Those 8 outputs form an 8-bit number, so there are exactly 256 rules. The boxes above show the table, and you can click any of them to flip that bit.
Rule 30 produces chaos from a single cell; Mathematica used it as a random number generator.Rule 90 draws a Sierpiński triangle. Rule 110 is Turing complete (Matthew Cook, 2004).Rule 184 is a toy model of traffic flow.