[ibab]

Great question! There is more to it than you can see in the animation. Because this is a quantum mechanical problem, it's not enough to take into account a single given field configuration at a given point in time, but we have to work with all possible field configurations at the same time. Because the number of configurations grows exponentially with the complexity of the system, we have to invest enormous amounts of memory and computing power into simulating it.

Feynman actually wrote this pretty amazing paper on the topic of simulating quantum mechanical systems with computers: http://link.springer.com/article/10.1007/BF02650179. You should have a look, it's quite readable!

(If the paywall is a problem for you, you should be able to find the paper elsewhere)

[ape4]

Thanks. Here it is without a paywall. https://people.eecs.berkeley.edu/~christos/classics/Feynman.... Such a simple title ;)