Fractal Breakdown Image of Every Outcome in Tic-Tac-Toe
The first player in tic-tac-toe, conventionally labelled X, has a choice of one of nine squares in which to place his marker. The opposing player O then has a choice of one of the remaining eight squares. On X's next turn again he has a choice of seven squares, and so forth. There are thus a total of 9! possible series of moves (9 factorial: 9 x 8 x 7 x ... x 1), giving us 9! possible tic-tac-toe games. Some of these are wins for X, some for O, and some draws (wins for neither player). The fractal image shown in Figure 1, sections of which are progressively enlarged in Figure 2, offers an analytic presentation of all possible tic-tac-toe games.
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