of 1.3 $h^{-1}$ Mpc. We emphasize that this highly-resolved box is much larger than the cluster at its center, and that therefore there are galaxies in a range of local densities. In Tonnesen & Cen (2012) we compare the local densities of galaxies in this refined region to a different refined region in the same large periodic box centered around a void, and showed that there is substantial overlap in the distribution of local densities found in the two very different large-scale environments.

We consider two refined simulations of the same region that differ in their level of maximum refinement. In the refined region in the low resolution simulation, the minimum cell size is 0.46 $h^{-1}$ kpc, using 11 refinement levels at $z = 0$. The initial conditions for the refined region include a mean interparticle separation of 117 $h^{-1}$ kpc comoving and a dark matter particle mass of 1.07$\times$10$^8$ $h^{-1}$ M$_\odot$. In the high resolution simulation, the minimum cell size is 0.114 $h^{-1}$ kpc, using 13 refinement levels at $z = 0$, with an initial mean interparticle separation of 58.6 $h^{-1}$ kpc comoving and a dark matter particle mass of 1.5$\times$10$^7$ $h^{-1}$ M$_\odot$. We only have the $z$$=$1 output 