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Tic Tac Au-Toe-Mata Mark Schiebel

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Outline I.Brief Cellular Automata Background II.Tic-Tac Au-Toe-Mata Rules III.Project Design IV.Computer Strategy V.Conclusion

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Cellular Automata Background A cellular automaton exists of a set of rules, a neighborhood, a set of states, and a lattice (or graph) Left + Mid + Right Mod 2 0 1 …… ……

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2-D Cellular Automata Up + Left + Mid + Right + Down Mod 2 No-Wrap ? Wrap

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Tic Tac Au-Toe-Mata Game 2-D Automata with no wrapping Beginning state is a checkerboard pattern Object is to get either 1s or 0s in a row Players alternate turns changing any 1 to a 0 or 0 to a 1 – This also inverts each cell in its neighborhood ={up, down, left, right}

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Tic Tac Au-Toe-Mata Initial positionAfter 1 move (row 3 col 2)

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Winning Player 1 wins Player 2 wins

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Project Requirements Program represents a two-player cellular automata game Program has an intelligent computer player (non-optimal) The user can change the number of players and the player names The user can see all previously made moves and undo moves indefinitely.

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Project Design The program is written in Java The program has an easy to use GUI The program is understandable by a general user (inclusion of help menu)

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Picture of Tic Tac Au-Toe-Mata

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Optimum Strategies An optimum strategy is one that will either win or produce the best possible result To find a good strategy, it is necessary to determine if a move is “good” or “bad” This can be done by determining how “good” a position is and how “good” the position a certain move creates is

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Strategy Implementation The strategy was implemented with a game tree. The game tree checked for winning or losing positions. A game tree requires a function to determine how good any position is.

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Game Tree Function Notice that by moving at position (3,3), player 1 can win the game with all 1s horizontally. Therefore, it is not necessarily good to optimize the number of cells in a given row or column. A better strategy is to maximize the total number of cells on the entire board.

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Game Tree ………….

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Questions

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