Thanks a lot, guys!
If I wanted to use an influence map for asymmetric movement costs or one-way movement, then I'd need to use a more sophisticated algorithm, I suppose? Traversing each location on the map through the map's topology, as with a traditional Dijkstra or A* algorithm? And that would be a lot slower, right? But if I just wanted non-grid-based movement, so long as it's symmetric (e.g. text adventure or MUD-style maps where you can go north, or south, or upstairs, or Dennis), the influence map would be just fine; I'd simply have a different definition of "neighbor"?
I suppose influence maps could also be used to generate terrain? I did something like that in my 2013 7DRL, "TriQuest" - I placed "hotspots" on the map, and designed "levels" of terrain such that higher level terrain would contain more dangerous monsters and might also be harder to traverse. (If you enter a "wasteland" terrain, expect very strong enemies!) But that was an open world, and I suppose it could also be used in a traditional dungeon, using the pathfinding algorithm to "dig" corridors between rooms?