  Bianchi models are posited by the BKL picture to be essential building blocks
towards an understanding of generic cosmological singularities. We study the
behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi
type VIII and IX, as they approach the big bang singularity. It is known since
2001 that generic Bianchi IX spacetimes converge towards the so-called
Mixmaster attractor as time goes towards the singularity. We extend this result
to the case of Bianchi VIII vacuum. The BKL picture suggests that particle
horizons should form, i.e. spatially separate regions should causally decouple.
We prove that this decoupling indeed occurs, for Lebesgue almost every Bianchi
VIII and IX vacuum spacetime.
