That's interesting, the path with random noise added to the weights looks much more optimal than straight up a*... a* moves north first then starts to skirt around the large lake system while the noise added algorithm just beelines for the hook turn around the lakes. Now, just to keep this in perspective, a person who did not know the lay of the land would do far worse than either a* or your modification. I would test your method on more varieties of terrain to see how it performs. If it's consistent you could use it to path-find for entities that possess knowledge of the lay of the land and use less optimal methods for entities that don't know anything about the terrain they are traveling over.