chaos and the LGP-30
Carlos E Murillo-Sanchez
ce.murillosanchez at gmail.com
Tue Jul 28 00:07:23 CDT 2020
Carlos E Murillo-Sanchez wrote:
> 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:
>>> 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.
>> Thanks! Looks like a really interesting read.
> 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.
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