We study finite and affine k-parabolic arrangements, a generalization of the k-equal arrangement for any finite reflection group or affine Weyl group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements. Khovanov (1996) gave an algebraic description for the fundamental group of the complement of the 3-equal arrangement. We generalize Khovanov's result to obtain an algebraic description of the fundamental group of the complement of any finite or affine 3-parabolic arrangement. Our arguments use the notion of discrete homotopy theory, due to Barcelo et al. This is joint work with Helene Barcelo and Christopher Severs.