How to create a 3D density map of a system of varying number of particles?
R packages misc3d and rgl. The function image3d in misc3d does what you need and is very parametrizable via rgl (change the transparency, the view angle, axes, etc...). I used it with fairly big arrays (~10000000 data points/plots) and it produced great 3D density plots.

Both R (e.g. package biOps) and Matlab (image processing toolbox) have very powerful tools for image analysis if you need to get for example RBG levels in your plots but as far as I understood, you have the 3D arrays containing the interaction values, right?

Matlab proposes similar tools if you prefer Matlab (don't remember the exact functions) over R and both will require a fair amount of RAM as the data must be loaded in the environment.

As your system is time dependent you can also create movies fairly easily if you wish so (e.g. rgl's movie3d function).

Here a quick example of a 3D density plot: