Lorenz attractor

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)