When you sign up for a PHD level color theory class at MIT a pack of crayola is required (I recommend the 128 pack with the built in sharpener, the 256 is just obscene). Now getting back to this riddle and forgetting some of the complicated math behind it; imagine givng directions not in terms of left and right, north or south, or x and y but in colors. And, why not.
Indulge me in my MS Paint drawn diagram. No matter what point you start at if you follow the pattern"Red-Blue-Blue---Red-Blue-Blue---Red-Blue-Blue" you will end up at the yellow dot.
If you flip it, and always go "Blue-Red-Red" you will always end up at the green dot.
(you've definitely already tried to stump it)
Imagine a city plan where no matther where you are you know how to get to the hospital or to the liquor store. Pretty fucking awesome if you ask me. Forget the GPS and that gruff voice that barks out directions, all we needs is ROYGBIV.