In the below cobweb diagram I am interested in why the iterations $( x_1,x_2,x_3)$ are marked when the 'cobweb' intersects the line $y=x$.
Image: https://i.stack.imgur.com/iiYST.png
For example, why does the 'cobweb' not go up to the point on $y=g(x)$ to get $x_3$? Is there any special reason for this or is it just convention?
I've tried looking on Wolfram MathWorld, various PowerPoints and .pdfs available online, and Wikipedia, yet non have an explanation (or even add these points).