{"id":"conways-game-of-life","domain":"recreational","type":"Concept","title":"Conway's Game of Life","slug":"conways-game-of-life","url":"/mathematics/recreational/conways-game-of-life/","invented":"1970, John Conway","summary":"Cellular automaton with 4 simple rules producing Turing-complete complex behaviour. Classic example of emergence.","rules":["Living cell with <2 living neighbours dies","Living cell with 2-3 living neighbours survives","Living cell with >3 living neighbours dies","Dead cell with exactly 3 living neighbours becomes alive"],"added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Berlekamp, E.R., Conway, J.H. and Guy, R.K. (2004). Winning Ways for Your Mathematical Plays. Vol. 4, 2nd ed. A K Peters."},{"tier":1,"citation":"Rendell, P. (2011). A Turing machine in Conway's Game of Life. In Game of Life Cellular Automata. Springer, pp. 339-380."},{"tier":2,"citation":"Gardner, M. (1970). Mathematical Games. Scientific American, 223(4), 120-123."},{"tier":3,"citation":"Wolfram, S. (2002). A New Kind of Science. Wolfram Media."}],"relationships":[{"type":"related_to","target":null,"label":"Turing completeness, Halting Problem"},{"type":"related_to","target":"graph-theory","label":"Graph Theory — grid structure"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.6"}