We analyse numerically the onset of pre-big bang inflation in an inhom
ogeneous, spherically symmetric Universe. Adding a small dilatonic per
turbation to a trivial (Milne) background, we find that suitable regio
ns of space undergo dilaton-driven inflation and quickly become spatia
lly at (Omega --> 1). Numerical calculations are pushed close enough t
o the big bang singularity to allow cross checks against previously pr
oposed analytic asymptotic solutions.