Tic Tac Au

Toe

Mata
Mark Schiebel
Outline
I.
Brief Cellular Automata Background
II.
Tic

Tac Au

Toe

Mata Rules
III.
Project Design
IV.
Computer Strategy
V.
Conclusion
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
1
0
0
1
1
0
1
…
…
1
0
0
1
1
0
1
…
…
2

D Cellular Automata
0
0
1
1
1
0
1
0
0
Up + Left + Mid + Right + Down Mod 2
1
0
1
1
0
0
0
0
0
No

Wrap
1
0
1
1
0
1
0
0
0
?
Wrap
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}
Tic Tac Au

Toe

Mata
Initial position
After 1 move
(row 3 col 2)
Winning
Player 1 wins
Player 2 wins
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.
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)
Picture of Tic Tac Au

Toe

Mata
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
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.
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.
Game Tree
………….
Questions
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