Having looked at this image, and having read other's take on it, here's my theory, which is similar to what I've been reading:
The picture represents the 3 stages of exploration of the galaxy.
1) One probe type is responsible for body discovery - the ADS if you like
2) Another probe is responsible for Detailed Surface Scanning - the DSS
3) The 3rd probe is responsible for sending that data back
The top and bottom circles with the seeming LAT/LON lines, represent the
same planet - i.e. judging by the depiction of the flowerships - the Thargoid's home planet.
So overall, the picture tells the story of 1) Sending the three probes out, 2) and recieving the data back from the probes.
We explorers do similar, except we send ourselves out in our ships, and we follow more or less the exact same sequence...
1) ADS honk
2) DSS
3) "Send" the data to Universal Cartographics (by selling them the data)
I think that's all this is - just a depiction of galaxy exploration.
Now, there is that additional centre point on the top and bottom planets -
either that means it's just a representation of the probes being sent out and data coming back to the Thargoid home world,
or it could be saying the probes are being sent out from these newly-discovered big bases, and the data is being returned to those bases - and from this data you get the resultant Thargoid version of a galaxy map.
My 2-pence worth, but I think it's as simple as that - the equivalent of our Voyager gold disks - design 'em to make it as simple as we think we can make it to help an alien intelligence understand what's on the disk.
I have my doubts that anything on that spectrograph represents pointers to somewhere in the galaxy. Maybe I'm wrong though - time will tell