1. Tic Tac Au-Toe-Mata Mark Schiebel

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

3. 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 …… ……

4. 2-D Cellular Automata Up + Left + Mid + Right + Down Mod 2 No-Wrap ? Wrap

5. 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}

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

7. Winning Player 1 wins Player 2 wins

8. 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.

9. 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)

10. Picture of Tic Tac Au-Toe-Mata

11. 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

12. 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.

13. 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.

14. Game Tree ………….

15. Questions