🚀 go-pugleaf

In article <gordon.721582896@tramp.Colorado.EDU> gordon@tramp.Colorado.EDU
(GORDON ALLEN R) writes:
>mrmarcel@eos.ncsu.edu (MICHAEL RONN MARCELAIS) writes:
>>Does anybody have the equations that Lorenz used in his old weather program? 
>>It was the first time he noticed the 'sensitive to initial conditions'
>>phenomenon that started research into Chaos.
>
>	dX/dt = a(Y-X)
>	dY/dt = bX-Y-XZ
>	dZ/dt = XY - cZ
>
>				where a = 10
>				      c = 8/3
>				      b = control parameter (try 28)

     These are indeed the Lorenz equations (as they are now known) but
these aren't the original weather simulation equations where Lorenz
noticed sensitive dependence on initial conditions.  Lorenz actually
started out with some specialized version of the Navier-Stokes equation
(a PDE) and noticed sensitive dependence in these equations under the conditions
of his weather simulation.  The Lorenz ODEs shown above are a truncation
of the Navier-Stokes equation for the special case of (I think)
Rayleigh-Benard convection under certain fairly restrictive conditions.
Lorenz cooked up these equations as a simple example of what he was
seeing in his more sophisticated weather models.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca