It is a cellular automata model, in fact. As for how they grow, its a simple stochastic process where once a cell overgrows another, it has a probability of success. If it succeeds, then one more cell location is added to the colony object, and the cell in the environment is set to the value of the colony. As to what constitutes a split, it is if two groups of cells which were once contiguous are no longer contiguous. E.g. I have two "species" in the following 3x3 environment

time=0
a a a
b a b
a a a

time=1
a a a
b b b
a a a
[download]

So, at t0, we have three colonies in the system, at t1, we have four, as the initial colony of species a is now two colonies due to the central link being overgrown by species 2, and there remain two colonies of b. Of note is that this is the similar to the following situation:

time=0
a a a
a b a
a a a

time=1
a a a
b b b
a a a
[download]

where the colony b in the center has expanded in two directions and severed both links. At t1 we have three colonies. As a sidenote as to why this is important to the simulation, colonies have aggregate properties depending on their size. Were I to not keep track of individual colonies, later dispersed cells would get the benefits of a larger colony size, even if they are no longer connected.

UPDATE: Note that in situation 1, there are three colonies at t0 and four at t1, not two at t0 as I had previously stated. The two cells labeled b are seperate colonies and do not merge at t1. Sorry for the confusion.