A typical kind of failure, illustrated in the pictures on the next page, is that points with coordinates determined by successive numbers from the generator turn out to be distributed in an embarrassingly regular way. At first, such failures might suggest that more complicated schemes must be needed if one is to get good randomness. And indeed with this thought in mind all sorts of elaborate combinations of linear congruential and other generators have been proposed. But although some aspects of the behavior of such systems can be made quite random, deviations from perfect randomness are still often found.
And seeing this one might conclude that it must be essentially impossible to produce good randomness with any kind of system that has reasonably simple rules. But the rule 30 cellular automaton that we discussed above demonstrates that in fact this is absolutely not the case.