Religion
In reply to the discussion: Religious Symbolism in the Islamic Prayer Rug [View all]MineralMan
(146,317 posts)Geometric patterns are common to both, and are pretty much automatic, given the grid-like limitations of woven fabrics. Religious and other symbolism are also aspects of both. However, one thing about weaving a rug, whether flat or pile, is that the limitations that exist, due to the physical structure of the weaving, restrict choices to some degree.
Colors are another interesting thing to compare. Both the early Navajo rugs and rugs of Asian origin used natural dyes, which are somewhat limited in the available color choices. So, you see similarities there, as well.
Design elements like borders, fields, and floating elements on those fields are also sort of dictated by the medium.
So, I'm not sure there's a cultural connection as much as a commonality out of the limits the medium imposes.
Like you, I've lived both in Turkey and in Arizona, so have been exposed to both, as well.