The Lorenz system is a model proposed by Edward Lorenz in 1963 to give a simplified modelization of convection rolls in the atmosphere, the three dimensional system proposed by Lorenz follows :

The Rayleigh-Benard convection problem
is described the velocity field __U__(__x__,t) and temperature field
T(__x__,t), where __x__ represents the point location, t the time,
__U__ the velocity at time t and location __x__ and T the temperature
at time t and location __x__.

In the Lorenz system, the *x*
coordinate is proportional to the velocity of the circulating flux, while
the ** z** coordinate represents the distortion of the temperature
with respect to a linear profile between the upper and the lower temperature.
The r parameter is the ratio between the Rayleigh number and the Critical
Rayleigh number, s is the Prandt number and b is the ratio between the
height of a roll and the length of two neighbour rolls.

The standard parameters are s=10.0, r=28.0 and b=2.66, they yield to a chaotic regime. This regime corresponds to a "strange attractor" called the Lorenz attractor.

I have written a matlab program to
calculate and plot in the three dimensional space the location of successive
points that evolve accordingly to the Lorenz system. This program can be
found here. Some of the plots obtained using this
program follow (the blue point represents the starting point, the black
one is the endding point.

On the upper image we can see that, for r=1, the point (0,0,0) is a stable equilibrium point.

On the upper image we can see the Lorenz strange attractor, with its two attracting points.