Lorenz equations
x' 
= 
s(yx) 
y' 
= 
Rxyxz 
z' 
= 
xyqz 
The above system of differential equations is known as Lorenz equations.
Lorenz equations exhibit chaotic behaviour.
Lorenz applet
You may use the applet above to experiment with the equations. To do so:

rearrange/resize the browser window so that the Lorenz window is clearly
visible.

Use the scroll bars to set the initial value (x0,y0,z0), the view angles
and the parameter R. (the remaining parameters are fixed to the classical
values s=10, q=8/3).

Press Show trajectory button to view the trajectory

Press Rotate button to rotate the trajectory  this gives a better
three dimensional visualization

Press Poincare button to see the intersection of the trajectory
with the Poincare plane z=R1

Select Use color to mark the y coordinate (the coordinate perpendicular
to the screen) with rainbow colors

Select Show two to simultaneously display two nearby trajectories

Use the lower two scroll bars to change the animation speed and the original distance between the
nearby trajectories
(c) Marian Mrozek, 19972001