A butterfly flaps its wings, and a hurricane hits somewhere many miles away. Can these two events possibly be related?

This popular adage is called #ButterflyEffect.

<Now, it must be stated that, in fact, the flapping of a butterfly’s wings is not actually known to be the reason for any natural disasters, but the idea of it does get at the driving force of Chaos Theory. The common theme among the two is the sensitive dependence on initial conditions.>

The butterfly effect has now become a common term to express any situation where a small change is supposed to be the cause of larger consequences.

Edward Lorenz described #chaos as:

When the present determines the future, but the approximate present does not approximately determine the future.

The butterfly effect, an underlying principle of chaos, describes how a small change in one state can result in large differences in a later state. 

 

A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.

Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such systems, rendering long-term prediction of their behavior impossible in general. 

Chaos is seen in natural systems like weather patterns and traffic patterns. Having this knowledge is important because it enables us to create better prediction tools for weather, or design roads in a more efficient way.

Well, now you know why the adage is so popular and how butterflies and math are connected!

Sources:

<1> The butterfly effect and the maths of chaos by Institue of Mathematics & its applications.

<2> Chaos: The Mathematics Behind the Butterfly Effect by James Manning.

<3> Google images.

#math #mathstories #story43 #butterfly #chaos