Editing Langton's ant (section)

==Modes of behavior==
These simple rules lead to complex behavior. Three distinct modes of behavior are apparent,<ref>{{cite book |last=Pratchett |first=Terry |title=The Science Of Discworld |title-link=The Science of Discworld |last2=Stewart |first2=Ian |last3=Cohen |first3=Jack |publisher=[[Ebury Press]] |year=1999 |isbn=978-0091865153}}</ref> when starting on a completely white grid.

#Simplicity. During the first few hundred moves it creates very simple patterns which are often [[Symmetry|symmetric]].
#Chaos. After a few hundred moves, a large, irregular pattern of black and white squares appears. The ant traces a [[Pseudorandomness|pseudo-random]] path until around 10,000 steps.
#Emergent order. Finally the ant starts building a recurrent "highway" pattern of 104 steps that repeats indefinitely.

All [[Finite-state machine|finite]] initial configurations tested eventually converge to the same repetitive pattern, suggesting that the "highway" is an [[attractor]] of Langton's ant, but no one has been able to prove that this is true for all such initial configurations. It is only known that the ant's trajectory is always unbounded regardless of the initial configuration<ref>{{cite journal |last1=Bunimovich |first=Leonid A. |last2=Troubetzkoy |first2=Serge E. |title=Recurrence properties of Lorentz lattice gas cellular automata |journal=Journal of Statistical Physics |volume=67 |issue=1–2 |pages=289–302 |year=1992 |doi=10.1007/BF01049035|bibcode=1992JSP....67..289B |s2cid=121346477 }}</ref>&nbsp;– this result was incorrectly attributed and is known as the [[E.G.D. Cohen|Cohen]]-Kong theorem.<ref>{{cite journal |last=Stewart |first=I. |title=The Ultimate in Anty-Particles |journal=Sci. Am. |volume=271 |pages=104–107 |year=1994 |issue=1 |doi=10.1038/scientificamerican0794-104 |bibcode=1994SciAm.271a.104S |url=http://dev.whydomath.org/Reading_Room_Material/ian_stewart/AntyParticles.pdf |access-date=6 May 2013 |archive-url=https://web.archive.org/web/20160303211426/http://dev.whydomath.org/Reading_Room_Material/ian_stewart/AntyParticles.pdf |archive-date=3 March 2016 |url-status=dead }}</ref>