chaos and the LGP-30

[Carlos E Murillo-Sanchez]

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:
>>> 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.
>
"dinosaur", argh.