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 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)
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