  We study the evolution of holographic screens, both generally and in explicit
examples, including cosmology and gravitational collapse. A screen $H$ consists
of a one-parameter sequence of maximal surfaces called leaves. Its causal
structure is nonrelativistic. Each leaf can store all of the quantum
information on a corresponding null slice holographically, at no more than one
bit per Planck area. Therefore, we expect the screen geometry to reflect
certain coarse-grained quantities in the quantum gravity theory.
  In a given spacetime, there are many different screens, which are naturally
associated to different observers. We find that this ambiguity corresponds
precisely to the free choice of a single function on $H$. We also consider the
background-free construction of $H$, where the spacetime is not given. The
evolution equations then constrain aspects of the full spacetime and the
screen's embedding in it.
