  The nature of generic spacelike singularities in general relativity is
connected with first principles, notably Lorentzian causal structure, scale
invariance and general covariance. To bring a new perspective on how these
principles affect generic spacelike singularities, we consider the initial
singularity in spatially homogeneous Bianchi type VIII and IX vacuum models in
Ho\v{r}ava-Lifshitz gravity, where relativistic first principles are replaced
with anisotropic scalings of Lifshitz type. Within this class of models,
General Relativity is shown to be a bifurcation where chaos becomes generic. To
describe the chaotic features of generic singularities in Ho\v{r}ava-Lifshitz
cosmology, we introduce symbolic dynamics within Cantor sets and iterated
function systems.
