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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
Lorenz attractor
(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 {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 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)