[[File:Gospers glider gun.gif|thumb|right|A single [[Bill Gosper|Gosper]]'s [[Gun (cellular automaton)|Glider Gun]] creating "[[Glider (Conway's Life)|gliders]]" in [[Conway's Game of Life]]]]
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Conway is especially known for the invention of the Game of Life, one of the early examples of a [[cellular automaton]]. His initial experiments in that field were done with pen and paper, long before personal computers existed.
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Since the game was introduced by Martin Gardner in ''[[Scientific American]]'' in 1970,<ref>{{Cite magazine|title=Mathematical Games: The fantastic combinations of John Conway's new solitaire game "Life"|first=Martin|last=Gardner|magazine=Scientific American|volume=223|date=October 1970|pages=120–123}}</ref> it has spawned hundreds of computer programs, web sites, and articles.<ref>{{Cite web |url=https://www.dmoz.org/Computers/Artificial_Life/Cellular_Automata/Conway%27s_Game_of_Life |title=DMOZ: Conway's Game of Life: Sites |access-date=11 January 2017 |archive-url=https://web.archive.org/web/20170317103511/http://www.dmoz.org/Computers/Artificial_Life/Cellular_Automata/Conway%27s_Game_of_Life/ |archive-date=17 March 2017 |url-status=dead }}</ref> It is a staple of recreational mathematics. There is an extensive [[wiki]] devoted to curating and cataloging the various aspects of the game.<ref>[http://www.conwaylife.com/wiki/Main_Page LifeWiki]</ref> From the earliest days, it has been a favorite in computer labs, both for its theoretical interest and as a practical exercise in programming and data display. At times Conway has said he hates the Game of Life–largely because it has come to overshadow some of the other deeper and more important things he has done.<ref>[https://www.youtube.com/watch?v=E8kUJL04ELA Does John Conway hate his Game of Life?] (video)</ref> Nevertheless, the game did help launch a new branch of mathematics, the field of [[cellular automata]].<ref>MacTutor History: The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of cellular automata.</ref>
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The Game of Life is now known to be [[Turing completeness|Turing complete]].<ref>Rendell (2015)</ref><ref name=case>Case (2014)</ref>