  The method of four-dimensional Causal Dynamical Triangulations provides a
background-independent definition of the sum over geometries in quantum
gravity, in the presence of a positive cosmological constant. We present the
evidence accumulated to date that a macroscopic four-dimensional world can
emerge from this theory dynamically. Using computer simulations we observe in
the Euclidean sector a universe whose scale factor exhibits the same dynamics
as that of the simplest mini-superspace models in quantum cosmology, with the
distinction that in the case of causal dynamical triangulations the effective
action for the scale factor is not put in by hand but obtained by integrating
out {\it in the quantum theory} the full set of dynamical degrees of freedom
except for the scale factor itself.
