  Using the power of numerical relativity, we show that, beginning from generic
initial conditions that are far from flat, homogeneous and isotropic and have a
large Weyl curvature, a period of slow contraction rapidly drives spacetime
towards vanishingly small Weyl curvature as the total energy density grows,
thus providing a dynamical mechanism that satisfies the Weyl Curvature
Hypothesis. We also demonstrate a tight correlation between the Weyl Curvature
Hypothesis and ultralocal behavior for canonical scalar fields with a
sufficiently steep negative potential energy density.
