Lorenz attractor

mathematics (After Edward Lorenz, its discoverer) A region

in the phase space of the solution to certain systems of

(non-linear) differential equations. Under certain

conditions, the motion of a particle described by such as

system will neither converge to a steady state nor diverge to

infinity, but will stay in a bounded but chaotically defined

region. By chaotic, we mean that the particle's location,

while definitely in the attractor, might as well be randomly

placed there. That is, the particle appears to move randomly,

and yet obeys a deeper order, since is never leaves the

attractor.

Lorenz modelled the location of a particle moving subject to

atmospheric forces and obtained a certain system of ordinarydifferential equations. When he solved the system

numerically, he found that his particle moved wildly and

apparently randomly. After a while, though, he found that

while the momentary behaviour of the particle was chaotic, the

general pattern of an attractor appeared. In his case, the

pattern was the butterfly shaped attractor now known as the

Lorenz attractor.

(1996-01-13)