Automata on a 2-dimensional tape

This paper explains our approach to the problem of pattern recognition by serial computer. The rudimentary theory of vision presented here lies within the framework of automata theory. Our goal is to classify the types of patterns that can be recognized by an automaton that scans a finite 2-dimensional tape. For example, we would like to know if an automaton can decide whether or not a given pattern on a tape forms a connected region. Although we have solved a number of problems, we have failed to solve this connectedness problem. This paper merely begins to describe the action of automata in higher dimensions. Our goal now is to generalize the theory presented here and make it applicable to a wide variety of pattern-recognizing machines.