The Bolshoi Simulation is the most accurate large-scale visualization/ simulation of the universe that exists (2011). It’s mapped everything that we know of, and a lot of what we don’t…
The Bolshoi supercomputers create this simulation of the large-scale structure of the universe by first examining the data from NASA’s WMAP explorer, which maps out the cosmic microwave background radiation.
Since this radiation is the light left over from the Big Bang, it’s the most ancient data in the universe, and from those starting conditions the supercomputer can use existing theoretical knowledge to simulate the evolution of different parts of the universe.
Because the supercomputer’s results match up almost perfectly with what we actually can observe of the history of the cosmos, astronomers are confident in its accuracy as a proxy for the actual universe.
There’s more information at io9 — really interesting stuff, and perhaps necessary to better explain the above visual fly-through to younger observers. There are also more details and simulations here on the project site.