I was looking at some 18th century French (I think) nautical charts of Spanish colonies that I found on the Spanish National Institute of Geography website, and a detail stroke me: all the lines that converge in different points in the map. Link. If you can't open it, here you have another example.
I don't see why the mapmaker would add this. It can't be related to some type of triangulation, and it actually obstructs the rest of the map. And as far as I know, these maps had an actual practical use, so it wouldn't have much sense to add unnecessary decoration.
Those lines are not there at random. When you start to look in detail, patterns will emerge. Let me explain.
Part of the points where many lines converge form a circle. From each of those points, 32 rays come out, and the figure is very important: those 32 lines are the rhumbs. Of course, there can be far more rhumbs, but 32 is the classic division and give enough precision as to help the captain or the first officer to map the route the ship is tracing. If you know the ship has travelled 12 leagues SSO, and then 20 SO, you only have to take up your set squares, move it parallel to the SSO rhumb and use the compass to mark 12 leagues. Afterwards, you do the appropriate thing for the other 20 leagues.vThis rhumb-line network comes from the portolan charts and it is very useful. Here you can see a good example:
https://upload.wikimedia.org/wikipedia/commons/a/ac/1311_portolan_of_Pietro_Vesconte.jpg
Besides this network, you have the vertical and horizontal lines, which are there to mark the latitude and longitude with regularity. Finally, you have diagonal lines, which are the bisectrices to the horizontal-vertical network. These lines are added there in order to help calculate angles and making sure your use of the set squares was correct.
So, in conclusion, those lines are all practical in nature, as they would help with the process of keeping an accurate track of a ship's route.
