Game of life animated glider 2

Glider - the simplest, but the most important pattern in Game of Life [1]

Conway's Game of Life, also known more simply as Life, was a computer simulation created by the British mathematician John Horton Conway in 1970. It was influenced by an idea proposed by the mathematician, John Von Neumann, of creating universal constructors that could build copies of itself. Conway looked to simplify Von Neumann's mathematical models to four rules that the Game of the Life should maintain.

  1. There should be no explosive growth.
  2. There should exist small initial patterns with chaotic, unpredictable outcomes.
  3. There should be potential for von Neumann universal constructors.
  4. The rules should be as simple as possible, whilst adhering to the above constraints.


The Game of Life is an infinite two-dimensional grid with square cells, that could be in either in a state of live or dead. Each cell is influenced by the state of its nearest eight neighbors, in the cardinal and diagonal direction. Four simple rules (based on models of population growth) dictate the state of any cell at a particular generation (each iteration of state):

Screen shot 2012-03-05 at 8.52.35 PM

A diagram showing the rules from the first publication of the Game of Life.

  1. Any live cell with fewer than two live neighbors dies. [Underpopulation]
  2. Any live cell with more than three live neighbors dies. [Overcrowding]
  3. Any live cell with two or three live neighbors continues to the next generation. [Stable populations]
  4. Any dead cells of exactly three live neighbors will come back to life. [Reproduction]

The seed, the first of the each system is determined by the player, but all subsquent generations are the result of the initial seed without any human interactions. In essence, the Game of Life is a zero-player game, where the course of the game doesn't require a player.


From the four simple rules, a vast variety of complex structures is possible. The majority of structures can be classified to: still lifes, oscillators, spaceships, and gun.

Still Lifes Edit

66px-Game of life block with border

Block [1]

82px-Game of life boat

Boat [1]

98px-Game of life beehive


98px-Game of life loaf



Game of life animated glider

Glider [1]

Game of life animated LWSS

Lightweight spaceship (LWSS)[1]


Game of life beacon


Game of life blinker

Blinker [1]

Game of life toad



Game of life pulsar




Gosper glider gun[1]


The creation of the Game of Life would herald the start of the field of cellular automaton. A field that combines technology with physics, mathematics, biology, and complexity science to model life in the virtual realm. It was a milestone in the sense that with only four simple rules and a two dimensional universe, scientists were able to create designs and complexity that rival that of life itself.

thumb|left|296px|Conway's Game of Life

An important part of Game of Life is the glider, which allowed information to be transmitted with a constant speed over long distance. In essence, it allowed the creations of counters and memory, which are the building blocks of a computer. It has been proven that the Game of Life is a universal Turing machine, meaning that if given infinite memory (in order to construct the structures needed) and infinite time, it can do any computation that a modern computer can do. Compared to other system, this isn't a trivial result. It represents a link between the computer world and the natural world, as the very rules that creates emergence is also inherent in computer structure. In fact, the idea that the Game of Life has both the potential of creating a Turing machine that is also a Von Neumann universal constructor makes the idea of grey goo, a hypothetical material that can self-replicate and be able to compute, possible.


A recent milestone in the Game of Life was the discovery of Gemini in 2010. It was a spaceship that was able to read off instruction from a trailing tape and creating a copy of itself above it, while destroying it's own copy. Even though this hasn't reach the ideal state of the Von Neumann universal constructor, it remains an important step in understand the complex nature of how replication works in a system and how best to emulate it.

thumb|left|300px|Gemini - the first self-replicating spaceship

The timespan between the creation of Life and the discovery of Gemini, some forty years, does highlight the inherent difficulty in creating something that has the ability to self-replicate, whether in nature or in a computer.

Additional ResourcesEdit

Java applet of Game of Life

A more comprehensive version of the Game of Life

Conwaywiki - a wiki dedicated to Game of Life

A news website about Game of Life


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