cover image

Butterfly effect

Idea that small causes can have large effects / From Wikipedia, the free encyclopedia

Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Butterfly effect?

Summarize this article for a 10 years old


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.

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 different 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.

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 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 engineer 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.