  How does inhomogeneity affect our interpretation of cosmological
observations? It has long been wondered to what extent the observable
properties of an inhomogeneous universe differ from those of a corresponding
Friedman-Lemaitre-Robertson-Walker (FLRW) model, and how the inhomogeneities
affect that correspondence. Here, we use numerical relativity to study the
behavior of light beams traversing an inhomogeneous universe and construct the
resulting Hubble diagrams. The universe that emerges exhibits an average FLRW
behavior, but inhomogeneous structures contribute to deviations in observables
across the observer's sky. We also investigate the relationship between angular
diameter distance and the angular extent of a source, finding deviations that
grow with source redshift. These departures from FLRW are important
path-dependent effects with implications for using real observables in an
inhomogeneous universe such as our own.
