A 1-dimensional cellular automaton which generates random sequences is discussed. Each site in the cellular automaton has value 0 or 1, and is updated in parallel according to the rule (). Despite the simplicity of this rule, the time sequences of site values that it yields seem to be completely random. These sequences are analysed by a variety of empirical, combinatorial, statistical, dynamical systems theory and computation theory methods. An efficient random sequence generator based on them is suggested.