We present the first results of hydrodynamical simulations that follow
the formation of galaxies to the present day in nearly spherical regions
of radius ~20h-1Mpc drawn from the Millennium Simulation
(Springel et al.). The regions have mean overdensities that deviate by
(-2, -1, 0, +1, +2)σ from the cosmic mean, where σ is the
rms mass fluctuation on a scale of ~20h-1Mpc at z = 1.5. The
simulations have mass resolution of up to
~106h-1Msolar, cover the entire range
of large-scale cosmological environments, including rare objects such as
massive clusters and sparse voids, and allow extrapolation of statistics
to the (500h-1Mpc)3 Millennium Simulation volume
as a whole. They include gas cooling, photoheating from an imposed
ionizing background, supernova feedback and galactic winds, but no AGN.
In this paper, we focus on the star formation properties of the model.
We find that the specific star formation rate density at z