Under certain conditions, the motion of a particle described by certain
systems 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 it never leaves
the attractor. Lorenz modeled the location of a particle moving subject
to atmospheric forces and obtained a certain system of ordinary
differential 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 behavior 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.
If you would like to download a picture of the Lorenz attractor, please go to our download section.