Will Cooke via cctalk wrote:
Theoriginal paper is
Edward N. Lorenz, "Deterministic Nonperiodic Flow", Journal of TheAtmospheric
Sciences,Vol. 20, March 1963, pp. 130-141.
It is at multiple locations in the web. One source is:
http://www.astro.puc.cl/~rparra/tools/PAPERS/lorenz1962.pdf
At Cornell I took John Guckenheimer's and Steve Strogatz's courses, inaddition
to the more EE-focused nonlinear systems course taught byHsiao-Dong Chiang.
Really beautiful stuff.
carlos.
Thanks! Looks like a really interesting read.
Will
What I think is most awesome, in terms of the role that computing held
in this discovery, is that mathematicians since the early 20th century
took as granted the idea that the "limit sets" of the trajectories of
solutions of time-differential equations were either periodic (also
called limit cycles) or singletons (stable or unstable equilibria at a
single point in space). Lorenz, through digital integration of a simple
third-order differential equation, proved that there were other kinds of
limit sets. These limit sets are distributed in space and occupy
geometries that we now call "fractal". When they are the result of a
chaotic solution to a differential equation, we call them "strange
attractors". The first one that was studied was Lorenz's strange
attractor, which, in 3D space, looks like a butterfly. I don't know if
there is any connection between its shape and the popular "butterfly
altering an initial airflow in the dynosaur's era" interpretation (by
the way, utterly dumb for anyone who knows about real-life nonlinear
dynamical systems). But what I do know, is that mathematicians had to
suddenly backtrack 50 years and try to understand how they could be so
wrong. And that's how chaos theory emerged. Thanks to numerical
computation.
carlos.
