  We compute the length of spacelike geodesics anchored at opposite sides of
certain double-sided flow geometries in two dimensions. These geometries are
asymptotically anti-de Sitter but they admit either a de Sitter or a black hole
event horizon in the interior. While in the geometries with black hole
horizons, the geodesic length always exhibit linear growth at late times, in
the flow geometries with de Sitter horizons, geodesics with finite length only
exist for short times of the order of the inverse temperature and they do not
exhibit linear growth. We comment on the implications of these results towards
understanding the holographic proposal for quantum complexity and the
holographic nature of the de Sitter horizon.
