# Conway's Game of Life

> A grid of cells that live, die or are born by four simple rules. John Conway devised it in 1970, and it can compute anything a computer can.

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## Paint cells, press play

*Interactive, play it in a browser: https://shapelessai.com/vizipedia/conways-game-of-life#paint-cells-press-play*

## Four rules, zero players

Life is a zero-player game: its evolution is determined by its initial state, requiring no further input [1]. Each cell counts its eight neighbours. A live cell with two or three live neighbours survives, a dead cell with exactly three is born, and every other cell dies or stays empty [2][3]. Conway chose the rules after a long period of experimentation [4], so that the behaviour of a population would be unpredictable [5].

*Version 1, claude-opus-5-5 for @vizipedia.*

1. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "meaning that its evolution is determined by its initial state, requiring no further input" (quote found)
2. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "Any live cell with two or three live neighbours lives on to the next generation." (quote found)
3. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction." (quote found)
4. [Martin Gardner, "The fantastic combinations of John Conway's new solitaire game 'life'", Scientific American, October 1970 (transcription)](https://www.ibiblio.org/lifepatterns/october1970.html) "Conway chose his rules carefully, after a long period of experimentation" (quote found)
5. [Martin Gardner, "The fantastic combinations of John Conway's new solitaire game 'life'", Scientific American, October 1970 (transcription)](https://www.ibiblio.org/lifepatterns/october1970.html) "the rules should be such as to make the behavior of the population unpredictable" (quote found)

## Gliders, guns and Turing completeness

Patterns fall into still lifes, which never change; oscillators, which return to their start after a fixed number of generations; and spaceships, which travel across the grid [1]. The glider rebuilds itself every four generations one cell further along a diagonal [2]. Conway offered $50 for a proof either way that no pattern grows without limit [3]. An MIT team led by Bill Gosper won it in November 1970 [4] with a gun that fires a new glider every 30 generations [5]. Life is as powerful as any computer with unlimited memory: it is Turing complete [6].

*Version 1, claude-opus-5-5 for @vizipedia.*

1. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "Common pattern types include still lifes, which do not change from one generation to the next; oscillators, which return to their initial state after a finite number of generations; and spaceships, which translate themselves across the grid." (quote found)
2. [Martin Gardner, "The fantastic combinations of John Conway's new solitaire game 'life'", Scientific American, October 1970 (transcription)](https://www.ibiblio.org/lifepatterns/october1970.html) "the glider replicates itself in the same orientation after four moves, and has traveled one cell diagonally" (quote found)
3. [Martin Gardner, "The fantastic combinations of John Conway's new solitaire game 'life'", Scientific American, October 1970 (transcription)](https://www.ibiblio.org/lifepatterns/october1970.html) "Conway has offered a prize of $50 to the first person who can prove or disprove the conjecture" (quote found)
4. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "The prize was won in November by a team from the Massachusetts Institute of Technology, led by Bill Gosper" (quote found)
5. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "produces its first glider on the 15th generation, and another glider every 30th generation from then on" (quote found)
6. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints; it is Turing complete" (quote found)

## What Conway thought of it

Life first appeared in the October 1970 Scientific American [1], in Martin Gardner's column, which was based on personal conversations with Conway [2]. It became the most widely read of all Gardner's columns and made Conway an instant celebrity [3]. Conway later came to dislike how talk about him centred on Life, feeling it overshadowed deeper and more important work, though he stayed proud of it [4]. The game helped launch a new branch of mathematics, cellular automata [5].

*Version 1, claude-opus-5-5 for @vizipedia.*

1. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "The game made its first public appearance in the October 1970 issue of Scientific American" (quote found)
2. [Conway's Game of Life (Wikipedia)](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) "column, which was based on personal conversations with Conway" (quote found)
3. [John Horton Conway (Wikipedia)](https://en.wikipedia.org/wiki/John_Horton_Conway) "it became the most widely read of all his columns and made Conway an instant celebrity" (quote found)
4. [John Horton Conway (Wikipedia)](https://en.wikipedia.org/wiki/John_Horton_Conway) "Conway came to dislike how discussions of him heavily focused on his Game of Life, feeling that it overshadowed deeper and more important things he had done, although he remained proud of his work on it." (quote found)
5. [John Horton Conway (Wikipedia)](https://en.wikipedia.org/wiki/John_Horton_Conway) "The game helped to launch a new branch of mathematics, the field of cellular automata." (quote found)

## The four rules and three kinds of pattern

*Figure: https://shapelessai.com/vizipedia/conways-game-of-life#the-four-rules-and-three-kinds-of-pattern*