Lovely graphic simulator of the effects of gravity on the universe, from simple two-body problems to colliding galaxies.
The Universe Sandbox.

[Click to enlarge. More screenshots here.]
Less than a decade ago, this was the province of room-sized supercomputers. Now available on your desktop.
I do so dearly love living in the future, although unfortunately, I haven’t been able to try this out for myself since it’s Windows-only. I have got to get around to setting up Wine or dual-boot.
Link from frequent commenter Chanda via email.