A Turing Machine is a state machine.
State machines come in various forms. The point is to transition from one state to another, each state encapsulating a behavior.

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Simply put, a Turing Machine takes in several strips of tapes, each having symbols written along it. There is a "head" that reads these tapes. When encountering a symbol, it refers to a table telling the machine what to do--stamp a new symbol next to the current one, switch which tape it is reading, or some combination of both.