Generalized Mobile Automaton


A generalized mobile automaton is a generalization of the mobile automaton in which the automaton may have more than one active cell. Generalized mobile automata allow for more change in a single update, so interesting behavior can develop more rapidly. Like cellular automata, the generalized mobile automata can involve parallel computing. During an updating event, every active cell is updated based on the value of that cell and its neighbors. The update determines the new color for the active cell, and specifies which if any of it and its neighbors become active cells. A cell becomes active if any of the previous step's events determined that it should become active. An example is shown above (Wolfram 2002, p. 76).

Its rule structure allows for the creation and destruction of the active cells, but only updates values of the active cells. This way there is no overlap, even if neighboring cells are active. A cellular automaton is a special case, where all the cells are active cells, and the outcome of all updates includes the instruction to make the cell and its neighbors active.

An example is one whose rules dictate the following. If the neighborhood of an active cell is either (white, white, white) or (black, white, white), then the active cell becomes black, and it and its neighbor to the right become active. Otherwise, the active cell becomes white, and neither it or its neighbors are made active. Suppose now that we begin with a background of white cells in a row, with the middle one active. The update then requires the middle cell to become black, and it and its neighbor to the right, which is a white cell, become active at the next step. Now there are two active cells. The middle cell has a neighborhood of (white, black, white), and the neighborhood of the other active cell is (black, white, white). From the active cell in the middle, the next update requires the middle cell to become white. Its neighbor to the right becomes black, and it and its neighbor to the right are active for the next update. And so on. The resulting evolution in this case is that the active cells, one black and one white, move consistently to the right, against a white background.

See also

Cellular Automaton, Mobile Automaton, Turing Machine

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This entry contributed by Todd Rowland

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Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 76-77, 2002.

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Generalized Mobile Automaton

Cite this as:

Rowland, Todd. "Generalized Mobile Automaton." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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