Behavior of Lorenz Attractor I'm trying to understand the behavior of the Lorenz attractor. I understand that it is very sensitive to initial conditions but I don't understand **WHAT** I'm looking at. So here are two lorenz attractor figures from matlab: !enter image description here !enter image description here The only difference between both of them is the initial condition of $x_2$ changes from 0 to -3. But I don't understand what is going on or how to describe it. In very amateuristic terms, I can say that the lorenz attract is showing heavy circulation on the right lobe of the first figure and low circulation in the left lobe but in the 2nd figure it's just the opposite.

What you are looking at is the trajectory of a particle that is moving in accordance with a fairly simple collection of equations. If the particle starts at $(-1,0,1)$, it traces out the curve in the first diagram; if it starts at $(-1,3,1)$, it traces out the second.

These two diagrams don't really illustrate "sensitive dependence on initial conditions". What that means is that even if two particles start out very near each other, say, one at $(-1,0,1)$ and the other at $(-1,.0001,1)$, they will only stay close for a little while, and then they will move very far apart (while staying on the attractor).

To see sensitive dependence, try < or <

What the two diagrams do show is how complex the individuals trajectories are.