For other uses, see Butterfly effect (disambiguation).
A plot of Lorenz's strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.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 conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
The term is closely associated with the work of mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the metaphorical 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.[1][2] He discovered the effect when he observed runs of his 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.[3]
The idea that small causes may have large effects in weather was earlier acknowledged by French mathematician and physicist Henri Poincaré. American mathematician and philosopher Norbert Wiener also contributed to this theory. Lorenz's work placed the concept of instability of the 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 deterministic chaos.[4]
The butterfly effect concept 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.
^"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" (PDF). Archived (PDF) from the original on 2022-10-09. Retrieved 23 December 2021.
^"When Lorenz Discovered the Butterfly Effect". 22 May 2015. Retrieved 23 December 2021.
^Lorenz, Edward N. (March 1963). "Deterministic Nonperiodic Flow". Journal of the Atmospheric Sciences. 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2.
^Rouvas-Nicolis, Catherine; Nicolis, Gregoire (4 May 2009). "Butterfly effect". Scholarpedia. Vol. 4. p. 1720. Bibcode:2009SchpJ...4.1720R. doi:10.4249/scholarpedia.1720. Archived from the original on 2016-01-02. Retrieved 2016-01-02.
In chaos theory, the butterflyeffect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear...
The ButterflyEffect is a 2004 American science fiction thriller film written and directed by Eric Bress and J. Mackye Gruber. It stars Ashton Kutcher...
The ButterflyEffect 2 is a 2006 American science fiction psychological thriller film directed by John R. Leonetti and starring Eric Lively, Erica Durance...
The butterflyeffect describes a phenomenon in chaos theory whereby a minor change in circumstances can cause a large change in outcome. The scientific...
substantial avalanche effect is one of the primary design objectives, and mathematically the construction takes advantage of the butterflyeffect. This is why...
13, 2021, Fetty Wap posted the cover art for his upcoming album The ButterflyEffect, six years following his debut; however on the intro, he sings "it's...
by Written by Original air date U.S. viewers (millions) 66 1 "The ButterflyEffect (Part 1)" John Terlesky Sheila Lawrence & Henry Alonso Myers October 16...
Spontaneous, unsolicited and uncritical imitation of another's behavior Butterflyeffect – Idea that small causes can have large effects Cascading failure –...
Atticus Lincoln. Carmack has also appeared in films, including The ButterflyEffect 3: Revelations, Into the Blue 2: The Reef, Love Wrecked, Beauty & the...
market, resulting in the adoption of further CSR initiatives. Butterflyeffect — an effect where a minimal change in one state of a system results in large...
John in Robin Hood, Jeeves Tremor in Smokin' Aces, and Carlos in The ButterflyEffect. He received a 2012 Best Supporting Actor Genie nomination for his...
of its ten seasons. Kutcher starred in the science fiction film The ButterflyEffect (2004) and had a voice role in Open Season (2006). Kutcher appeared...
also had a brief career as a solo singer when she released the album ButterflyEffect (2014). Roberts has presented various television shows, including Ant...
Hilborn, Robert C. (April 2004). "Sea gulls, butterflies, and grasshoppers: A brief history of the butterflyeffect in nonlinear dynamics". American Journal...
expansion Butterflyeffect Chain reaction Clapotis Domino effect Katamari Damacy, a video game based on the snowball effect Matthew effect Positive feedback...
(2012–2017). She has also appeared in films such as The Untold (2002), The ButterflyEffect 2 (2006), and Painkillers (2015). Durance was born in Calgary to parents...
She had a lead role opposite Ashton Kutcher in the sci-fi drama The ButterflyEffect (2004). Smart co-starred with Ryan Reynolds and Anna Faris in Just...
of Arcadia and Ghost Whisperer, as well as a part in the films The ButterflyEffect and Stick It.[citation needed] In 2006, Amedori starred in Fox's drama...
January 26, 1993) is a Canadian actor. He has appeared in the films The ButterflyEffect, Godsend, Birth, Running Scared, Ultraviolet, X-Men: The Last Stand...
Blackwood Mountain when their lives are threatened. The game features a butterflyeffect system in which players must make choices that may change the story...
in Vulgar, Ashton Kutcher's goth college roommate "Thumper" in The ButterflyEffect, American football player Louie Lastik in Remember the Titans, Johnny...
Global Information