30 years ago, astronomers started playing around with making simulations of colliding galaxies. Computers were slow, so they could only keep track of a few hundred or thousand stars, which limited the models severely. The software had to keep track of every star, its location, velocity, and mass... the number of calculations is forbidding. Things have come a long way. Now astronomers can track millions of stars using hydrodynamics codes, and then graphically display them giving them color, adding in dust, the effects of cloud collisions, supernovae... and the results are stunning. Have a look. This is not just some animation; this is an actual result using complicated math and physics. It's also lovely. You can read more about this here.
Tip o' the spiral arm to Pamela Gay, aka StarStryder, who is reporting from the IAU meeting in Rio.