The direction of the line tends to move from the "stronger" point to the "weaker" and towards the one closest to an edge of the frame.
This relationship between two points in a frame, thus the strength of the line connecting them together, becomes weaker when the background increases in complexity.
I took two images from a golf course. The first is a of a putter. The quality of the image is not great but it demonstrates the power of the relationship as the eye naturally looks from the golfer's feet to the hole.
See first the image as taken:
The feet are lighter and bigger so is naturally the stronger point. The eye naturally moves from left to right anyway and will also naturally want to see where the ball is heading.
I have added the arrow below to demonstrate this:
A more subtle case is the golf holes:
The flag catches the eye making it the stronger point but less obvious than the first example.
Lastly I used an image taken from the garden.
This time I left some colour in deliberately to see if the effect of the colour of the flower in an otherwise desaturated image would balance the greater size of the piece of wood, and I would say it does. There is a clear implied line between the two made more pronounced by the almost finger like positioning of the jagged edge of the wood. The wood is the stronger point by virtue of size and the jagged edge but not by much.
As an example of where both points attract equal attention is below:
I think the eye is attracted equally to the swings and tends to flick from one to the other.
Lastly, a shot of just two eyes was taken.
As the course notes suggests, the eye has a problem resolving the composition, quite distracting.
