The green cube on the map represents an expensive tile. The higher the stack of green cubes, the more expensive it is to step on that tile.
In my observations of A* expansion, I noticed that it sometimes did not shy away from stepping on a high-cost tile if it meant getting closer to the goal.
When I tweaked the heuristic to prioritize the goal above everything else, A* behaved like a greedy BFS. Conversely, if the heuristic for finding the goal was loosened, A* behaved more like Dijkstra's algorithm.