Sunday, February 21, 2010

Chaos Theory



















What Is Chaos?

In everyday language "chaos" implies the existence of unpredictable or random behavior. The word usually carries a negative connotation involving undesirable disorganization or confusion. However, in the scientific realm this unpredictable behavior is not necessarily undesirable. The scientific meaning of chaos can be summed up in the following statement:

"Chaos often breeds life, when order breeds habit."
– Henry Adams

Chaos is indeterminism at its best — a concept totally foreign and unwelcome in Laplace's world. The scientific usage of the word was first coined by Yorke and Li in their ground breaking paper, "Period Three Implies Chaos (1975)," in which they described particular flows as chaotic.

In short, chaos embodies three important principles:

* extreme sensitivity to initial conditions
* cause and effect are not proportional (!)
* nonlinearity