  Recently, studies of the gravitational collapse of a scalar field within
spherically symmetric AdS spacetimes was presented in
\cite{Bizon:2011gg,Jalmuzna:2011qw} which showed an instability of pure AdS to
black hole formation. In particular, the work showed that arbitrarily small
initial configurations of scalar field evolved through some number of
reflections off the AdS boundary until a black hole forms. We consider this
same system, extended to include a complex scalar field, and reproduce this
phenomena. We present tests of our numerical code that demonstrate convergence
and consistency. We study the properties of the evolution as the scalar pulse
becomes more compact examining the asymptotic behavior of the scalar field, an
observable in the corresponding boundary CFT. We demonstrate that such BH
formation occurs even when one places a reflecting boundary at finite radius
indicating that the sharpening is a property of gravity in a bounded domain,
not of AdS itself. We examine how the initial energy is transferred to higher
frequencies --which leads to black hole formation-- and uncover interesting
features of this transfer.
