Lamination languages

Leaves of laminations can be symbolically represented by deforming them into paths of labeled embedded carrier graphs, including train tracks. Here, we describe and characterize the languages of two-way infinite words coming from this kind of coding, called lamination languages, first, by using carrier graph sequences, and second, by using word combinatorics. These characterizations generalize those existing for interval exchange transformations. We also show that lamination languages have ultimately affine factor complexity, and we present effective techniques to build these languages.