[s-macke]

You can also use it to solve labyrinths. Just put a high pressure at the beginning and a low pressure at the end. Solve the Poisson equation. The path through the labyrinth is always the steepest slope. In [1] you can see a small implementation of the idea.

[1] https://simulationcorner.net/maze/

[setr]

More generally, I believe this is exactly the same as flow-field pathfinding, which conveniently has the property that you end up with a solution to the whole map -- so you've solved all pathfinding for all entities anywhere in the map, in one shot. Great for hosting a ridiculous amount of entities on a static (or slow-changing) map.

Brogue's creator also "invented" djikstra maps, which I believe is also exactly the same[0][1], to handle AI strategic pathfinding (e.g. avoid hazards while reaching treasure).

In Game AI Pro (I forget which article/book), someone suggests taking AI preferences (e.g. hunger, health) and computing a flow-field per preference (e.g. a food-map, a danger-map, etc), and multiplying the values against the preference to act as a weight (so food-map * %hunger, danger-map * %health), and summing the maps together to produce the final map used for pathfinding. Notably, the food-map can be shared by all entities consuming the same kind of food -- only the weight has to be re-calculated, and the final sum.

[0] http://www.roguebasin.com/index.php?title=The_Incredible_Pow...

[1] http://www.roguebasin.com/index.php/Dijkstra_Maps_Visualized