The movie above is a simulation of the formation of a spiral galaxy, based on a program described by Gould, Tobochnik, and Christian in their book 'An Introduction to Computer Simulation Methods'. Each of the cells in the simulation (which roughly correspond to the individual blobs that you can see in the movie) is a cluster of stars and each cluster is about 300 light years across. So this is a large simulation! This entire galaxy is about 30,000 light years in diameter which is not particularly large for a spiral galaxy, but it is quite a large system to simulate in a few seconds on a laptop - the complete simulation took about 100 seconds. (Making the movie took a bit longer...)
The basis for the calculation is the fact that an exploding star has a good chance of setting up the conditions for star formation in its vicinity, through the explosive shockwave that it sends out into space. This is coupled with the notion that the constituent rings of the galaxy move at constant velocity. With these assumptions the sprial and globular form of the galaxy emerges and evolves with time. (Like the distances, the time scales are vast, each timestep in the simulation is 107 years.)
You can perform very much more detailed simulations of galaxy formation, should the fancy strike you. But even this relatively simple model allows you to test the key facts and forces which are sufficient to explain the shape of spiral galaxies. Armed with the model, and its parameters, you can set about clarifying the key features which determine the different shapes of real galaxies, and even, if you are ambitious, the chances of the galaxy calming down and ceasing to produce new stars.
It turns out that the long range structure of the galaxy can be explained with only nearest neighbor interactions (if by nearest neighbor you mean cells about 300 light years across).