Tic Tac Au-Toe-Mata

1. Tic Tac Au-Toe-Mata Mark Schiebel

2. Outline • Brief Cellular Automata Background • Tic-Tac Au-Toe-Mata Rules • Project Design • Computer Strategy • Conclusion

3. 0 1 … … … … Left + Mid + Right Mod 2 Cellular Automata Background • A cellular automaton exists of a set of rules, a neighborhood, a set of states, and a lattice (or graph)

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

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 position After 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 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. Notice that by moving at position (3,3), player 1 can win the game with all 1s horizontally.

14. Game Tree ………….

15. Questions