A simple model for convection in the atmosphere with parameters r=27,s=10,b=8/3, model studied by the meteorogist Edward Lorenz. The variable x>0 indicates that the convective cell rotates in the direct sense and x<0 in the inverse sense. The system has a chaotic behavior and  demostrates that weather can not be predicted only from statistical data and needs model simulation.

# Lorenz equations

init x=1,y=2

param r=27,s=10,b=2.66666

x'= s*(-x+y)

y'= r*x-y-x*z

z'=  -b*z+x*y

done

more information: Wikipedia Lorenz atractor page

Another mechanical interpretation of the system is the rotation of a wheel under gravity with recipients that become heavier as they receive sand from the top of the wheel and lighter as they lost sand at a constant rate. Here we see the wheel and the ball follows the Lorenz’s attractor.

When the blue point is on the right side the wheel rotates in the direct sense (x>0), when the blue ball is on the left the wheel rotates in the inverse sense. It is impossible to predict with long term accuracy the change in the sense of rotation, this is the so called butterfly effect.