chaos and the LGP-30

[Carlos E Murillo-Sanchez]

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.