Editing Conway's Game of Life (section)

==Origins==

[[Stanisław Ulam]], while working at the [[Los Alamos National Laboratory]] in the 1940s, studied the growth of crystals, using a simple [[Lattice model (physics)|lattice network]] as his model.<ref name="pickover">{{cite book|author=Pickover, Clifford A.|title=The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics|url=https://archive.org/details/mathbookfrompyth00pick|url-access=limited|page=[https://archive.org/details/mathbookfrompyth00pick/page/n410 406]|year=2009|publisher=Sterling Publishing Company, Inc|isbn=978-1402757969}}</ref> At the same time, [[John von Neumann]], Ulam's colleague at Los Alamos, was working on the problem of [[self-replicating system]]s.<ref name="Schiff">{{cite book|last=Schiff|first=Joel L.|title=Cellular Automata: A Discrete View of the World|year=2011|publisher=Wiley & Sons, Inc|isbn=9781118030639|url=https://books.google.com/books?id=uXJC2C2sRbIC}}</ref>{{rp|1}} Von Neumann's initial design was founded upon the notion of one robot building another robot. This design is known as the kinematic model.<ref>John von Neumann, "The general and logical theory of automata," in [[Lloyd A. Jeffress|L.A. Jeffress]], ed., Cerebral Mechanisms in Behavior – The Hixon Symposium, John Wiley & Sons, New York, 1951, pp. 1–31.</ref><ref>{{cite journal|last1 = Kemeny|first1 = John G.|year = 1955|title = Man viewed as a machine|journal = Sci. Am.|volume = 192|issue = 4|pages = 58–67|doi=10.1038/scientificamerican0455-58|bibcode = 1955SciAm.192d..58K}}; ''Sci. Am.'' 1955; 192:6 (errata).</ref> As he developed this design, von Neumann came to realize the great difficulty of building a self-replicating robot, and of the great cost in providing the robot with a "sea of parts" from which to build its replicant. Von Neumann wrote a paper entitled "The general and logical theory of automata" for the [[Lloyd A. Jeffress#The Hixon Symposium|Hixon Symposium]] in 1948.<ref>{{Cite book |last=Von Neumann |first=John |title=Collected works. 4: Continuous geometry and other topics |date=1976 |publisher=Pergamon Press |isbn=978-0-08-009566-0 |edition=Repr |location=Oxford [u.a.] Frankfurt}}</ref> Ulam was the one who suggested using a ''discrete'' system for creating a reductionist model of self-replication.<ref name="Schiff" />{{rp|3}}<ref name="cadu">{{Cite book|title=Cellular Automata: A Discrete Universe|first=Andrew|last=Ilachinski|publisher=World Scientific|year=2001|isbn=978-981-238-183-5|url=https://books.google.com/books?id=3Hx2lx_pEF8C}}</ref>{{rp|xxix}} Ulam and von Neumann created a method for calculating liquid motion in the late 1950s. The driving concept of the method was to consider a liquid as a group of discrete units and calculate the motion of each based on its neighbours' behaviours.<ref>{{cite book|first1=Iwo|last1=Bialynicki-Birula|first2=Iwona|last2=Bialynicka-Birula|title=Modeling Reality: How Computers Mirror Life|year=2004|publisher=[[Oxford University Press]]|isbn=978-0198531005}}</ref>{{rp|8}} Thus was born the first system of cellular automata. Like Ulam's lattice network, [[Von Neumann cellular automata|von Neumann's cellular automata]] are two-dimensional, with his self-replicator implemented algorithmically. The result was a [[Von Neumann universal constructor|universal copier and constructor]] working within a cellular automaton with a small neighbourhood (only those cells that touch are neighbours; for von Neumann's cellular automata, only [[orthogonal]] cells), and with 29 states per cell. Von Neumann gave an [[constructive proof|existence proof]] that a particular pattern would make endless copies of itself within the given cellular universe by designing a 200,000 cell configuration that could do so. This design is known as the [[tessellation]] model, and is called a [[von Neumann universal constructor]].<ref name="TSRA">{{cite book|last1=von Neumann|first1=John|last2=Burks|first2=Arthur W.|title=Theory of Self-Reproducing Automata|url=https://archive.org/details/theoryofselfrepr00vonn_0|year=1966|publisher=[[University of Illinois Press]]}}</ref>

Motivated by questions in mathematical logic and in part by work on [[Simulation video game|simulation games]] by Ulam, among others, [[John Horton Conway|John Conway]] began doing experiments in 1968 with a variety of different two-dimensional cellular automaton rules. Conway's initial goal was to define an interesting and unpredictable cellular automaton.<ref name=":2" /> According to [[Martin Gardner]], Conway experimented with different rules, aiming for rules that would allow for patterns to "apparently" grow without limit, while keeping it difficult to ''prove'' that any given pattern would do so. Moreover, some "simple initial patterns" should "grow and change for a considerable period of time" before settling into a static configuration or a repeating loop.<ref name=":0" /> Conway later wrote that the basic motivation for Life was to create a "universal" cellular automaton.<ref>Conway, private communication to the 'Life list', 14 April 1999.</ref>{{better source needed|date=March 2022|reason=A "private communication" to a mailing list might not be impossible to verify, but it's pretty hard.}}

The game made its first public appearance in the October 1970 issue of ''[[Scientific American]]'', in [[Martin Gardner]]'s "[[Mathematical Games (column)|Mathematical Games]]" column, which was based on personal conversations with Conway. Theoretically, the Game of Life has the power of a [[universal Turing machine]]: anything that can be computed [[algorithm]]<nowiki/>ically can be computed within the Game of Life.<ref name="chapman">It is a model and simulation that is interesting to watch and can show that simple things can become complicated problems.{{cite web|url=http://www.igblan.free-online.co.uk/igblan/ca/|title=Life Universal Computer|author=Paul Chapman|access-date=12 July 2009|date=11 November 2002|archive-date=6 September 2009|archive-url=https://web.archive.org/web/20090906014935/http://www.igblan.free-online.co.uk/igblan/ca/|url-status=dead}}</ref><ref name="bcg">{{Cite book|last1=Berlekamp|first1=E. R.|author1-link=Elwyn Berlekamp|last2=Conway|first2=John Horton|author2-link=John Horton Conway|last3=Guy|first3=R. K.|author3-link=Richard K. Guy|title=Winning Ways for your Mathematical Plays|publisher=A K Peters Ltd|edition=2nd|year=2001–2004|title-link=Winning Ways for your Mathematical Plays}}</ref> Gardner wrote, "Because of Life's analogies with the rise, fall, and alterations of a society of living organisms, it belongs to a growing class of what are called 'simulation games' (games that resemble real-life processes)."<ref name=":0"/>

Since its publication, the Game of Life has attracted much interest because of the surprising ways in which the patterns can evolve. It provides an example of [[emergence]] and [[self-organization]].<ref name=":2"/> A version of Life that incorporates random fluctuations has been used in [[physics]] to study [[phase transition]]s and [[Nonequilibrium statistical mechanics|nonequilibrium dynamics]].<ref>{{Cite journal|last1=Alstrøm|first1=Preben|last2=Leão|first2=João|date=1994-04-01|title=Self-organized criticality in the ''game of Life''|url=https://link.aps.org/doi/10.1103/PhysRevE.49.R2507|journal=[[Physical Review E]]|volume=49|issue=4|pages=R2507–R2508|doi=10.1103/PhysRevE.49.R2507|pmid=9961636|bibcode=1994PhRvE..49.2507A}}</ref> The game can also serve as a didactic [[analogy]], used to convey the somewhat counter-intuitive notion that design and organization can spontaneously emerge in the absence of a designer. For example, philosopher [[Daniel Dennett]] has used the analogy of the Game of Life "universe" extensively to illustrate the possible evolution of complex philosophical constructs, such as [[consciousness]] and [[free will]], from the relatively simple set of deterministic physical laws which might govern our universe.<ref>{{cite book|last=Dennett|first=D. C.|date=1991|title=Consciousness Explained|location=Boston|publisher=Back Bay Books|isbn=978-0-316-18066-5|url-access=registration|url=https://archive.org/details/consciousnessexp00denn}}</ref><ref>{{cite book|last=Dennett|first= D.C.|date=1995|title=Darwin's Dangerous Idea: Evolution and the Meanings of Life|url=https://archive.org/details/darwinsdangerous0000denn|url-access=registration|location=New York|publisher= Simon & Schuster|isbn= 978-0-684-82471-0}}</ref><ref>{{cite book|last=Dennett|first= D.C.|date=2003|title=Freedom Evolves|location=New York|publisher=Penguin Books|isbn =978-0-14-200384-8}}</ref>

The popularity of the Game of Life was helped by its coming into being at the same time as increasingly inexpensive computer access. The game could be run for hours on these machines, which would otherwise have remained unused at night. In this respect, it foreshadowed the later popularity of computer-generated [[fractal]]s. For many, the Game of Life was simply a programming challenge: a fun way to use otherwise wasted [[Central processing unit|CPU]] cycles. For some, however, the Game of Life had more philosophical connotations. It developed a cult following through the 1970s and beyond; current developments have gone so far as to create theoretic emulations of computer systems within the confines of a Game of Life board.<ref>{{cite web|url=http://rendell-attic.org/gol/tm.htm|title=A Turing Machine in Conway's Game of Life|author=Paul Rendell|date=January 12, 2005|access-date=July 12, 2009|archive-date=April 17, 2019|archive-url=https://web.archive.org/web/20190417075720/http://rendell-attic.org/gol/tm.htm|url-status=live}}</ref><ref>{{cite web|url=https://conwaylife.com/wiki/Spartan_universal_computer-constructor|title=Spartan universal computer-constructor|author=Adam P. Goucher|publisher=LifeWiki|access-date=December 5, 2021}}</ref>