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Turning Cellular Automata into Multiplayer Games

A cellular automaton consists of a regular grid of cells, each in one of a finite number of states such as on and off. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously.

A “glider gun” in Conway’s Game of Life

It is characteristic of many cellular automata, e.g., Conway’s Game of Life pictured above, that relatively simple rules for the evolution of one state to another generate a high degree of emergent complexity. For instance, the rules for the Game of Life are as follows. A live cell is “on” and a dead cell “off,” and the “neighbors” each cell interacts with are the eight adjacent cells.

  1. Any live cell with fewer than two live neighbours dies, as if by underpopulation.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overpopulation.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

Notably, emergent complexity is also a highly praised feature of many games; a game like Go, for instance, has deep emergent strategy from a simply set of rules. Conway’s Game of Life as it stands is not really a game, or if it is, it is what is sometimes called a 0-player game. In other words, there are no players making moves, that is, changing the game state in the course of its evolution. But it already possesses a quality we care about in games. So this raises the following question for me: Can an emergently complex automata like the Game of Life be transformed into an emergently complex multiplayer game?

I plan to pursue this question in following posts, where I will document my attempt to turn Conway’s automaton into a game, but likely this is not the sort of task that can only be accomplished in one particular way, and I challenge the reader to make a stab at it too!

As we know from The Turk, a mechanical automaton can contain hidden life!

The Turk, an elaborate hoax exhibited as a chess automaton in the late 18th and early 19th centuries.

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