What is Butterfly effect: Definition and 16 Discussions

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 Lorenz. He noted that 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 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.The idea that small causes may have large effects in weather was earlier recognized by French mathematician and engineer Henri Poincaré. American mathematician and philosopher Norbert Wiener also contributed to this theory. Edward 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.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.

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  1. wrobel

    The Butterfly Effect: Small Changes Lead to Big Results

    Just an effect interesting to think about:
  2. B

    I Another butterfly making tornadoes thread

    Butterfly effect. Much ado about (almost) nothing. Not a lot has to be said to introduce the subject of course. But once before I addressed whether, in reality, a butterfly flapping its wings could actually create a tornado. My view essentially was that the degree of disturbance of the local...
  3. S

    Butterfly Effect: How much can you do before change occurs?

    I didn't know where to put this, but sci-fi seemed fitting: Just a hypothetical regarding the Butterfly Effect that's been puzzling me, if anyone has any insight... How much could you do in the past before your very presence started affecting history? For fun, let’s say you wake up 12 years...
  4. J

    What Determines the Zig Zag Pattern of Lightning?

    In a discussion about lightning destroying electronics on sailboats the issue of controlling lightning came up. One member (Baluncore) proposed that lightning is completely predictable. I've been taught that lightning is somewhat random. To me, random implies non-linear equations with sensitive...
  5. U

    Lorentz Chaos - The 'Butterfly Effect'

    Homework Statement Given the lorentz system for ##\sigma=10, b = \frac{8}{3}, r = 28##, and ##x(t)## from the first lorentz system, show that we can solve for y(t) and z(t) for the modified lorentz system by finding ##\dot E##.[/B] Homework EquationsThe Attempt at a Solution I have found...
  6. N

    What does the quantum butterfly effect tell us?

    I'm interested in interpretations and comments regarding this Wikipedia snippet:http://en.wikipedia.org/wiki/Butterfly_effect#Examples This idea is new to me. My limited understanding is that the macroscopic butterfly effect is related to non linear system effects...and slightly different...
  7. jk22

    The Butterfly Effect: Exploring Energy Conservation

    In chaos theory the image of a butterfly starting to fly in australia could lead to a hurricane in the usa is sometimes given to illustrate the sensivity to initial conditions. However I am struck with the energy conservation, a butterfly having a tiny energy and a hurricane a huge one. So...
  8. B

    Does the butterfly effect apply in reality?

    Everyone has heard that a butterfly flapping it's wings in one place may ultimately cause a tornado to form in another place. I really have a problem with this. It has also been said that if all the molecules in a cup of coffee were to move the same direction at the same time that the coffee...
  9. Loren Booda

    Butterfly Effect ever observed?

    How much influence does the Butterfly Effect have in our proximity? Even the Sun's planetary orbits, over billions of years, having experienced myriad nonlinear small interactions (here the "butterflies"), have seemingly resulted in very few chaotic catastrophic outcomes (hence "effects").
  10. I

    Butterfly effect from .01 degree temperature uncertainty

    I've always been curious about the boundary between the quantum and classical regimes, and I've often wondered if the weather is not just a chaotic system, but if it had a degree of true randomness, if it is significantly influenced by quantum events. So I tried to calculate the approximate...
  11. G

    Enigma of the butterfly effect

    I am trying to understand the so called "butterfly effect". http://en.wikipedia.org/wiki/Butterfly_effect By wording used to describe it, audience gains an intuitive impression that a small initial action of some sort can produce very large changes in system including unleashing storms that...
  12. G

    Dynamical systems: celestial mechanics, Poincare, Laplace, butterfly effect

    There is a work in history of astronomy I've been preparing for the most of the time in living memory. I can't say is it late, or due, or long, but counting from the 3 books I've seen, the one in focus of some private interest is Michael Hoskin "Cambridge Illustrated History of Astronomy"...
  13. Darryl

    Is the Butterfly Effect a True Phenomenon in Real-World Systems?

    The Butterfly Effect, "The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior...
  14. Schrodinger's Dog

    Re: the butterfly effect.

    http://www.doubleedgefilms.com/spin/player.html Short film. I found this while browsing around and I think it's really amusing. Sort of a philosophy students wet dream? What would you do? And do you think you might ever be able to stop?:smile: Made on a budget of $500. EDIT...
  15. C

    Mathematics of the butterfly effect

    What are some of the mathematical concepts used in the idea of the butterfly effect? Is there any thought that such a system would have a limit at which point all events beyond said limit are not considered part of the system designated by the initiating event? thanks
  16. R

    Butterfly Effect Movie's implications on our reality

    Hi, I just saw The Butterfly Effect in theaters yesterday after much much resistance... and i thought it was a GREAT movie... i don't know if the actual movie was great but the perspective on reality is what got me the most... In this movie, whenever he reads a passage from one of his...