Seems to work well, although I can't tell much without obstacles in the way to trip it up.
However, I am seeing some aesthetically odd results.
Nine steps, yes, it's technically an acceptable path, and one of the shortest paths, but visually it's not the shortest path (just one of the shortest options given the tiles).
Maybe you can add in a distance check, such that it will choose the shortest path that also *looks like* the shortest path, in that it's also the shortest linear distance?
Just an idea.
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