Laminations are classic sets of disjoint and non-self-crossing curves on surfaces.
Lamination languages are languages of two-way infinite words which code laminations by
using associated labeled embedded graphs, and which are subshifts. Here, we characterize
the possible exact affine factor complexities of these languages through bouquets of
circles, i.e. graphs made of one vertex, as representative coding graphs.
We also show how to build families of laminations together with corresponding lamination
languages covering all the possible exact affine complexities.