Code 10

Rule 30 is by many measures the simplest cellular automaton that generates randomness from a single black initial cell. But there are other simple examples—that historically I noticed slightly earlier than rule 30, though did not study—that occur in k = 2, r = 2 totalistic rules. And indeed among the 64 such rules, 13 show randomness. An example shown below is code 10, which specifies that if 1 or 3 cells out of 5 are black then the next cell is black; otherwise it is white.