How do I make influence map effects?

Specifically I'm talking about these types of influence maps, is it the same as fog of war or is there something more complicated going on here? How do I get the coloured borders to expand and merge into each other like they do in these screenshots? I quite like that effect.

https://i.ytimg.com/vi/1sN6LQykAdM/maxresdefault.jpg

http://tententacles.com/wp-content/uploads/2016/11/Powers2.png

 

Bumping this if it's okay because I'd quite like an answer on this particular subject.

 

Dynamically generate the mesh and merge the outlines via shader. This should get you started: https://forum.unity.com/threads/merge-sprites-by-color.172037/

With a little imagination, you can see that's exactly how Endless Space did it: https://techgage.com/reviews/gaming/endless_space/endless_space_16.jpg

 

Thanks! Yes, that looks exactly like what I'm looking for, ahhh, now it all makes a bit more sense, the influence is being scaled up and the border works in an uneven way because they're blending into each other.