  In this article, we study subword complexity of colorings of regular trees.
We characterize colorings of bounded subword complexity and study Sturmian
colorings, which are colorings of minimal unbounded subword complexity.
  We classify Sturmian colorings using their type sets. We show that any
Sturmian coloring is a lifting of a coloring on a quotient graph of the tree
which is a geodesic or a ray with loops possibly attached, thus a lifting of an
"infinte word". We further give a complete characterization of the quotient
graph for eventually periodic ones.
