A while ago I saw an image like the one below in a lecture, which was supposed to represent a rail network in a (square) city:

The circles represent trains that are moving either North/South or East/West along the vertical and horizontal tracks. The purpose of this picture was to show that, even though the grid is unevenly spaced, it is always possible to schedule the trains so that connections were perfectly timed: that is, any time a train arrives at an intersection, there is another train also arriving at that intersection, in a perpendicular direction.

The math behind this is very simple, so my question is: what is the area of study in which one would encounter an image like this?

configuration spaceswill be able to formalize this. Please note that I am not saying that the connection of this problem to configuration spaces is clear and canonical, but I think that 'configuration space' is the 'direction in knowledge space' in which you should go, possibly asking someone working in this direction. $\endgroup$ – Peter Heinig Sep 25 '17 at 11:46manymathematical pictures and mathematical exhibitions, haveneverseen this before, and find it a pleasure to see. I think that (copies of) this should be 'inducted' into, simultaneously, the Mathematikum, the MoMath, and the ix-quadrat. Seriously. $\endgroup$ – Peter Heinig Sep 25 '17 at 15:31