Butterfly effect

As Butterfly Effect (english butterfly effect ) refers to the effect that a large sensitivity consists in complex, non-linear dynamic systems on small variations in the initial conditions. Slightly different initial conditions can result in long-term course to a completely different development. There is this, a pictorial illustration of this effect on the example of the weather, which is eponymous for the butterfly effect: " Can the flap of a butterfly's wings in Brazil set off a tornado in Texas? "

The metaphor is problematic in that some people view the butterfly effect as a synonym for the snowball effect, increase in the small effects of a chain reaction itself. However, this is not meant here, but that small differences can change a whole system completely unpredictable and long term.

• 4.1 Fiction
• 4.2 movie
• 4.3 TV series

Origin of the name

The catchy term butterfly effect comes from the American meteorologist Edward N. Lorenz, who in 1972 before the American Association for the Advancement of Science a lecture entitled Predictability: Does the Flap of a Butterfly 's Wings in Brazil set off a tornado in Texas? held. However, he used the flapping wings of a seagull instead of the butterfly in its original form.

Scientific background

Preparatory work on the theory made ​​Lorenz with a work from 1963, in which he undertook a calculation to weather forecasting to the computer. He examined in the context of long-term weather forecasts for a simplified convection model the behavior of liquids or gases in heating them; Here, first forming rollers ( hot gas rises on one side, loses heat and decreases on the other hand again ), which become unstable with further supply of heat. This behavior he characterized on the basis of three linked differential equations. He projected the numerical result in the phase space and got that strange attractor, which became known as the Lorenz attractor later: an infinitely long trajectory in three-dimensional space, which does not intersect itself and has the form of two butterfly wings. Lorenz came across the chaotic behavior of his model by chance. To save computing time, he had resorted calculations already carried out in the numerical solution of the equations o a intermediate results, but only considers three decimal places, even though the computer calculated with an accuracy of six decimal places. The result was increasing differences over time between the old and new calculations, which Lorenz moved to his statements about the sensitivity to initial conditions. From nearly the same starting point diverged weather turns, until they finally showed no commonality.

In his first calculation he gave a start value for an iteration to six decimal places to ( 0.506127 ) in the second calculation to three ( 0.506 ), and although these values ​​differed by only about 1/10000 of one another, more later in this calculating the time from the first sharply.

The butterfly effect occurs in systems exhibiting deterministic chaotic behavior. These systems have the property that perform arbitrarily small differences in the initial conditions ( Clinamen ) over time to significant differences in the system; so they are sensitive, depending on the initial values.

Examples

Meteorology

Since the initial conditions can be determined experimentally always only with finite precision, a consequence of this effect is of such systems, it is impossible to predict their behavior for a long time. For example, the weather for a day can be predicted relatively accurately, whereas the prediction for a month is hardly possible. Even if the whole surface of the earth would be covered with sensors, they only slightly away from each subject, ranging up to the highest layers of the atmosphere and accurate data provided, would be an infinitely powerful computer will not be able to make long-term, accurate forecasts of weather conditions. Since the computer model does not capture the spaces between the sensors, there will be minor differences between model and reality, which then reinforce positive and lead to big differences. Example, you can make reasonably reliable predictions over a period of four days from the data of 1000 weather stations. For corresponding predictions For eleven days we would need 100 million already distributed evenly over the earth stations. Absurd is the project, if the prediction is to extend over a month; because then 1020 weather stations would be required, ie one on each five square millimeter surface (Ref.: Gentiles ). However, the Lorenz model is actually much more chaotic than the actual course of the weather. The equations are much more stable than the basic physical equations. The mathematician Vladimir Arnold Igorewitsch are as a principled upper bound for the weather forecast at two weeks.

Tent Figure

As an example of the butterfly effect, the tent figure is for reference.

It is plotted against the number of iterations, the difference between two such drawings. Both figures have the same control parameters, but slightly different starting values ​​. Thus, the effect occurs, the control parameters must be set so that the tent Figure chaotic behavior (indicated in the corresponding bifurcation diagram ).

As starting values ​​were chosen 0.506 and 0.506127. The maximum deviation is ± 1 Both figures are therefore completely different after a few iterations.

Planetary orbits

If more than two celestial bodies are gravitationally bound together, can lead to large changes in the orbits and positions nichtvorhersagbaren minimal changes to the initial situation over time. This behavior is the subject of the three- body problem.

Artistic processing

Fiction

• Ray Bradbury's short story of Thunder from 1952 concerned a good ten years before the emergence of the concept with the effect of small changes in the future.
• Michael Crichton 's novel Jurassic Park processed in this principle.
• Nick McDonell mentioned the butterfly effect in his novel Twelve.
• Stephen Fry relates in his book Making History in the butterfly effect.
• Jussi Adler -Olsen cites the term modified in the title of his thriller expectancy. The Marco effect. and explicitly refers to.

Film

• Blind Chance in 1981
• Run Lola Run of 1998
• She loves him - she does not love him the 1998
• Donnie Darko from 2001
• Minority Report with Tom Cruise Steven Spielberg 's 2002
• Radicals from 2003
• Category 6 - Day of the Tornado of 2004
• Butterfly Effect, Butterfly Effect 2 The Butterfly Effect 3 - Revelation from the years 2004, 2006 and 2009
• A Sound of Thunder from 2005
• Chaos in 2005
• Babylon from 2006
• Mr. Nobody from 2009

TV series

• Scrubs episode My Butterfly ( Season 3, Episode 16)
• Heroes, Episode The Butterfly Effect ( Season 3, Episode 2 )
• How I Met Your Mother, a result at the right time at the right place ( Season 4, Episode 22)
• Dexter, Episode Butterfly Effect ( Season 3, Episode 8)
• The Simpsons Treehouse of Horror V, aftermath and punishment
• Family Guy, Episode Permit, Lois Quagmire ( Season 5, Episode 18)
• Fringe - Special cases of the FBI, the firefly episode ( Season 3, Episode 10)
• Community, Episode Remedial Chaos Theory ( Season 3, Episode 4)
• Guilty Crown episode The convergence of the Butterfly Effect ( Season 1, Episode 22)