Research Activities > Research Introduction > What is Cellular Automaton?

What is Cellular Automaton?


What is Cellular Automaton?

Game of Life

Are you familiar with Conway’s Game of Life? As the name suggests, it is a game that represents the beginning of life and prosperity and is a typical example of a cellular automaton. Though it is called a game, it is not the kind of game where you control a player to go on adventures and fight with monsters. Instead, it is more like a simulation game where you develop cities. Let us explain the concept of cellular automata through the Game of Life.

Like many simulation games, the spaces on a grid are the stage of this game. The characters that appear in this game are nameless lives. One life can exist per square (also called a cell) on this grid. Every step (or turns as it is called in a simulation game) represents a generation of these lives. These lives interact with surrounding lives and transition to the next generation (step).

M.Gardner, “Mathematical Games – The fantastic combinations of John Conway’s new solitaire game “life”,” Scientific American, 223, 1970, pp.120-123

The Rules of the Game of Life

Most animals cannot live alone. However, when there are too many in one spot, they may end up dying from too few resources or from fighting with one another. In the Game of Life, the following four rules control the interactions between these lives.


If there are three lives neighboring a square with no life in it (also known as a dead cell) in any direction top, bottom or diagonally touching it, it can create a new life in the following generation (step).


If there are two to three lives neighboring a cell with a life in it (also known as a live cell), then those lives can survive to the next generation (step).


When there is fewer than one life neighboring a live cell, the lives will not survive due to under-population.


When there are more than four lives neighboring a live cell, the lives will not survive due to over-population.

What Makes the Game of Life Interesting?

The results of the Game of Life very much depend on the initial placement of the lives. Depending on how you place the lives, the lives may survive for a very long time or may just die off quickly. One aspect that makes this game interesting is the attempt to find an initial placement that will keep the lives alive for a very long time.

The image below is one example of the Game of Life. Generally, the square with a life (the live cell) is represented in black, and those which do not have a life are expressed using white. By following the rules mentioned above, you will be able to see the process of life and death play out. There are many placements of lives that have been discovered, and you will be able to see more examples on Wikipedia and other sites.

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Research Activities > Research Introduction > What is Cellular Automaton?

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