  The first part of this paper discusses general procedures for finding
numerical approximations to distinguished Kahler metrics, such as Calabi-Yau
metrics, on complex projective manifolds. These procedures are closely related
to ideas from Geometric Invariant Theory, and to the asymptotics of high powers
of positive line bundles. In the core of the paper these ideas are illustrated
by detailed numerical results for a particular K3 surface.
