  We present a simple example of a supersymmetric attractor mechanism in the
purely open string context of D-branes embedded in curved space-time. Our
example involves a class of D3-branes embedded in the 2-charge D1-D5 background
of type IIB whose worldvolume contains a 2-sphere. Turning on worldvolume
fluxes, these branes carry induced (p,q) string charges. Supersymmetric
configurations display a flow of the open string moduli towards an attractor
solution independent of their asymptotics. The equations governing this
mechanism closely resemble the attractor flow equations for supersymmetric
black holes in closed string theory. The BPS equations take the form of a
gradient flow and describe worldvolume solitons interpolating between an AdS_2
geometry where the two-sphere has collapsed, and an attractor solution with
AdS_2 x S^2 geometry. In these limiting solutions, the preserved supersymmetry
is enhanced from 4 to 8 supercharges. We also discuss the interpretation of our
solutions as intersecting brane configurations placed in the D1-D5 background,
as well as the S-duality transformation to the F1-NS5 background.
