  The parallel chip-firing game is an automaton on graphs in which vertices
"fire" chips to their neighbors when they have enough chips to do so. The game
is always periodic, and we concern ourselves with the firing sequences of
vertices. We introduce the concepts of motorized parallel chip-firing games and
motor vertices, study the effects of motors connected to a tree and show that
motorized games can be transformed into ordinary games if the motors' firing
sequences occur in some ordinary game. We then characterize exactly which
periodic firing patterns can occur in an ordinary game and state some
implications of the finding.
