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Bully automaton
A bully automaton is an ad-hoc extension of a cellular automaton in which certain state transitions, while occurring, can also unilaterally force other, non-adjacent cells to assume certain state transitions.
The name comes from the idea that the one cell "bullies" the other cells around, regardless of those cells' circumstances. This bullying typically leads to very complex interactions; it may or may not, for example, cause a chain reaction of state changes, depending on how the rules are defined.
The first language to employ a bully automaton is probably RUBE. Its successor, RUBE II, uses a more regular and predictable (but still as of yet unformalized) approach. ODDBALL can be described as a meta-language for defining bully automata.