It would seem probable that tartan could have been "invented" in many places either simultaneously or at different times with no cultural interaction. But isn't it interesting to think that in spite of outwardly different cultures that in so many places people are having the same ideas? Facetiously, I'd say that tartan might possibly have been invented by God and given to humans. No one can say when the idea to make little box-shaped patterns was spawned, but it must have been on the second or third day after the first person wove cloth.