The pictures below then show how the average density evolves in systems (c) and (d). And what is striking is that even though at the lowest level both of these systems consist of discrete cells, the overall distribution of density that emerges in both cases shows smooth continuous behavior.

And much as in physical systems like fluids, what ultimately leads to this is the presence of small-scale apparent randomness that washes out details of individual cells or molecules—as well as of conserved quantities that force certain overall features not to change too quickly. And in fact, given just these properties it turns out that essentially the same overall continuum behavior always tends to be obtained.

One might have thought that continuum behavior would somehow rely on special features of actual systems in physics. But in fact what we have seen here is that once again the fundamental mechanisms responsible already occur in a much more minimal way in programs that have some remarkably simple underlying rules.