How does this aspect of visual perspective work?

Say you are looking at the calm reflective surface of a pond, and as you walk by its bank the moon’s reflection follows you. At every step of your path the moon’s reflection has changed position on the water’s surface, but presumably it would still look the same from the other positions on your path. Why doesn’t the moon look like a stripe then? Is it verysmall differences in the surface? What is happening here?