I will argue that Lorentzian causal structure, general covariance, and scale invariance are first principles that play a key role for the nature of generic spacelike singularities in GR. To contextualize and bring a new perspective to the role of these first principles for some of the chaotic aspects of generic spacelike singularities, I will consider spatially homogeneous Bianchi type VIII and IX models in Horava-Lifshitz gravity, thus breaking and replacing relativistic first principles with anisotropic scalings of Lifshitz type. It turns out that GR in this context corresponds to a bifurcation where chaos becomes generic. For models that are different than the critical GR case, Cantor sets turn out to play a key role. In addition I will give examples that illustrate connections between spacelike singularities and weak null singularities, and I will also discuss permanent and recurring spikes.