What is Conway's Game of Life?

The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game: its evolution is determined entirely by its initial state, so nobody makes moves after the starting pattern is set. There is no win condition and no limit on the number of generations, apart from available computing resources. A person creates a starting configuration and then watches how it changes in discrete time steps called generations. [1]

The game is played on an infinite two-dimensional grid of square cells, each of which is either live or dead. Every cell looks at its eight neighbours, the cells touching it horizontally, vertically or diagonally. At each step, a live cell with fewer than two live neighbours dies, which is called underpopulation. A live cell with two or three live neighbours survives. A live cell with more than three live neighbours dies, which is called overpopulation. A dead cell with exactly three live neighbours becomes alive, which is called reproduction. [1] [2] [3]

These rules are applied simultaneously to every cell, and each generation is a pure function of the one before it. The rules are summarised by the rulestring B3/S23, where the numbers before the slash are the neighbour counts that cause a birth and those after it are the counts that allow survival. The starting pattern is called the seed. [1] [2]

Patterns are classified by behaviour. Still lifes do not change from one generation to the next. Oscillators return to their initial state after a finite number of generations. Spaceships translate themselves across the grid. People have been searching for patterns that evolve in interesting ways for over 50 years. [1] [4] [3]

The game was first simulated by hand, and computer simulations followed soon after. Modern programs such as Golly often avoid storing cells as simple two-dimensional arrays and use algorithms such as Hashlife, which represent patterns as a tree structure. [1]

According to Martin Gardner, as relayed in the Wikipedia article, Conway tried different rulesets looking for one in which some patterns would apparently grow without limit while it stayed hard to prove that any given pattern would. He also wanted some simple starting patterns to change for a considerable time before settling into a static form or a repeating loop. Conway later wrote that the basic motivation was to create a universal cellular automaton, though that source is flagged as needing a better citation. Plus magazine says he was really after an infinitely programmable computer. [1] [2]

The game is widely used as an example of emergent complexity, where very simple rules lead to varied, highly organised and hard-to-predict behaviour. One course page notes that some cellular automata, including the Game of Life, can be shown to be universal Turing machines. The idea of cellular automata dates to the 1940s, when Stanislaw Ulam and John von Neumann developed it to model self-replication, and the University of Waterloo's Computer Museum says Conway's game helped spread interest in the subject beyond academia. [5] [6] [4]

The game has also inspired many Life-like cellular automata, such as Highlife and Seeds, as well as variants with more than two states or non-square grids. [1]