Editing Butterfly effect (section)

{{short description|Idea that small causes can have large effects}}
{{Other uses}}
[[File:Double pendulum simultaneous realisations.ogv|thumb|upright=1.25|Experimental demonstration of the butterfly effect with six recordings of the same [[double pendulum]]. In each recording, the pendulum starts with almost the same initial condition. Over time, the differences in the dynamics grow from almost unnoticeable to drastic.]]

In [[chaos theory]], the '''butterfly effect''' is the sensitive dependence on [[initial condition]]s in which a small change in one state of a [[deterministic system|deterministic]] [[nonlinear system]] can result in large differences in a later state.

The term is closely associated with the work of the mathematician and meteorologist [[Edward Norton Lorenz]]. He noted that the butterfly effect is derived from the example of the details of a [[tornado]] (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant [[butterfly]] flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972.<ref name=":1">{{cite web |title=Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas? |url=https://mathsciencehistory.com/wp-content/uploads/2020/03/132_kap6_lorenz_artikel_the_butterfly_effect.pdf |access-date=23 December 2021 |url-status=live |archive-url=https://ghostarchive.org/archive/20221009/https://mathsciencehistory.com/wp-content/uploads/2020/03/132_kap6_lorenz_artikel_the_butterfly_effect.pdf |archive-date=2022-10-09}}</ref><ref>{{cite web |url=https://www.bbvaopenmind.com/en/science/leading-figures/when-lorenz-discovered-the-butterfly-effect/ |title=When Lorenz Discovered the Butterfly Effect |date=22 May 2015 |access-date=23 December 2021}}</ref> He discovered the effect when he observed runs of his [[numerical weather prediction|weather model]] with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.<ref name=":0">{{cite journal |last=Lorenz |first=Edward N. |title=Deterministic Nonperiodic Flow |journal=Journal of the Atmospheric Sciences |date=March 1963 |volume=20 |issue=2 |pages=130–141 |bibcode=1963JAtS...20..130L |doi=10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2 |doi-access=free}}</ref>

The idea that small causes may have large effects in weather was earlier acknowledged by the French mathematician and physicist [[Henri Poincaré]]. The American mathematician and philosopher [[Norbert Wiener]] also contributed to this theory. Lorenz's work placed the concept of ''instability'' of the [[atmosphere of Earth|Earth's atmosphere]] onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing [[nonlinear dynamics]] and [[chaos theory|deterministic chaos]].<ref name="scholarpedia">{{cite encyclopedia |last1=Rouvas-Nicolis |first1=Catherine |last2=Nicolis |first2=Gregoire |title=Butterfly effect |encyclopedia=[[Scholarpedia]] |date=4 May 2009 |volume=4 |issue=5 |page=1720 |bibcode=2009SchpJ...4.1720R |doi=10.4249/scholarpedia.1720 |doi-access=free |url=http://www.scholarpedia.org/article/Butterfly_effect |access-date=2016-01-02 |url-status=live |archive-url=https://web.archive.org/web/20160102214427/http://www.scholarpedia.org/article/Butterfly_effect |archive-date=2016-01-02}}</ref>

The concept of the butterfly effect has since been used outside the context of weather science as a broad term for any situation where a small change is supposed to be the cause of larger consequences.