  In this paper we construct a detailed map from pure and mixed half-BPS states
of the D1-D5 system to half-BPS solutions of type IIB supergravity. Using this
map, we can see how gravity arises through coarse graining microstates, and we
can explicitly confirm the microscopic description of conical defect metrics,
the M=0 BTZ black hole and of small black rings. We find that the entropy
associated to the natural geometric stretched horizon typically exceeds that of
the mixed state from which the geometry was obtained.
