One-dimensional binary automata are allowed to interact with each other using a 2×2 binary payoff matrix. In this way, chaotic evolution can be controlled or chaos can be induced (anticontrol). For each matrix, a hierarchy of the automata can be established as follows: an automaton with a higher rank controls (or anticontrols) an automaton with a lower rank. For some matrices and some rule number intervals, the ranking depends monotonically on the rule number.CMMFONDAPFONDAP