Butterfly effect

The butterfly effect is an idea from chaos theory. A small change can sometimes make much bigger changes happen.

Weather is hard to forecast, but that doesn't mean that when a butterfly flaps its wings in Tokyo, then a tornado will occur in Tennessee. However, what seem to be tiny changes in a planet's orbit can cause big changes to the weather: see Milankovich cycle.

More information

Author Ray Bradbury wrote the short story "A Sound of Thunder" with this idea— time travelers make a very small change in the past that makes a large change in the present. However, remember that time travel is impossible, or at least has never been shown to be possible.

One small incident may have a big impact on the future. There is no general theory which tells us what is going to happen.

Butterfly Effect Media

• 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.

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  A Battus polydamas butterfly in Brazil

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  Created by XaosBits using Mathematica and POV-Ray. The blue image is one trajectory of the Lorenz system with (σ, ρ, β) = (10, 28, 8/3) started from the initial point (0, 0, 1). The yellow image is for the same parameters but a different initial condition, (0, 0, 1+ε) where ε = 10-5.

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  LorenzCoordinatesSmall

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  A plot of Lorenz' 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.

Related pages

• Chaos theory
• Edward N. Lorenz