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Newcomers Start Here: The Hitchhiker's Guide to the Galaxy

What is Conway's Game of Life?

Conway's Game of Life is not a traditional game, instead, it is a "zero player game" where the outcome is determined by the initial state. Life is a cellular automaton developed by the eponymous British mathematician John Horton Conway. First, let's understand what cellular automaton means. Cellular automata can take many forms, but they typically consist of a grid of cells (in Life's case, a grid of squares) that change state every generation based on the state of neighboring cells. Cellular automata can range from extremely complex, with dozens of states and many rules governing the cells' behavior, to extremely simple. Life, thankfully, falls on the simpler side. In Life, cells only have two states, on or off. The state of a cell is determined by the 8 neighboring cells surrounding it. Knowing this information, Life's rules can be described very succinctly; 1. If a living cell has 2 or 3 neighbors, it will survive. 2. If a dead cell has exactly 3 neighbors, it will be born. 3. All other live cells die in the next generation, and all other dead cells stay dead.

Conway developed the Game of Life because he was interested in creating simple cellular automata with complex and unpredictable behavior. Despite being extremely simple and wholly deterministic (in other words, there is no randomness involved), Life has warranted 50 years (and counting) of intense study based on its properties.

There are three basic kinds of patterns in the Game of Life:

• Still lives, which do not change from generation to generation and are generally uninteresting, but sometimes interact with other patterns in a useful way
• Oscillators, patterns that repeat after a number of generations
• Spaceships, patterns that move indefinitely across the board of the Game of Life.

There exist a whole range of other patterns, however. For example, puffer are spaceships that leave a "trail" of debris behind it, and gun are patterns that repeatedly "fire" spaceships.

Why is Conway's Life interesting?

Firstly, it is important to examine what Conway was looking for when he made the Game of Life. Conway wanted to avoid two common types of cellular automata - those that collapse into static, predictable patterns almost immediately, and those that violently explode into uncontrollable chaos. Instead, he wanted it to be highly difficult to determine whether an initial pattern would survive, keep expanding, or die out. While we now know that most small, chaotic patterns stabilize, many of them take hundreds or thousands of generations to actually do so. This makes Life a clear example of order emerging from chaos, as well as an example of complex behavior emerging from simplistic rules.

Additionally, many small patterns in Life can react with other patterns, enabling the construction of engineered patterns. In fact, it is possible to build a computer in the Game of Life, and it has been long proven to be Turing Complete (in layman's terms, Life is theoretically capable of computing anything your computer can). Many small patterns have non-obvious uses. The glider, the smallest spaceship in Life, can be used to construct other patterns and can also function as a memory tape. The block, a 2x2 cube, has many reactions with other patterns and is used in many guns. There are many small still lives known as eaters which can stabilize various patterns and destroy, or "eat", spaceships.

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