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 byusing associated labeled embedded graphs, and which are subshifts. Here, we characterizethe possible exact affine factor complexities of these languages through bouquets ofcircles, i.e. graphs made of one vertex, as representative coding graphs.We also show how to build families of laminations together with corresponding laminationlanguages covering all the possible exact affine complexities.