  We will present a complete set of equations, in the form of an
Einstein-Bianchi system, that describe the evolution of generic smooth lattices
in spacetime. All 20 independent Riemann curvatures will be evolved in parallel
with the leg-lengths of the lattice. We will show that the evolution equations
for the curvatures forms a hyperbolic system and that the associated
constraints are preserved. This work is a generalisation of our previous paper
arXiv:1101.3171 on the Einstein-Bianchi system for the Schwarzschild spacetime
to general 3+1 vacuum spacetimes.
