  We show that, given any finite dimensional, connected, compact metric space
Z, there exists a group G acting geometrically on two CAT(0) spaces X and Y, a
G-equivariant quasi-isometry f from X to Y, and a geodesic ray c in X, such
that the closure of f(c), instersected with the boundary of Y, is homeomorphic
to Z. This characterizes all homeomorphism types of "geodesic boundary images"
that arise in this manner.
