When that applet first started, I thought it was the ants building piles problem. The piles problem is canonical in questions of bottom-up intelligence - it's a problem of dispersed coordination.
Say you have a bunch of grains of sand, evenly distributed, and you want them piled up. To to this, a (centralized, monolithic intelligence) would simply start moving all of the grains to a single spot on the board. If the person was coordinating ants to do the job, he might tell each ant to move a particular grain from Point A to Point B.
However, the same effect can be brought about by simply encoding each ant with two trivial rules, and using the idea of stimergy to coordinate them: If you run into a grain of sand and you're not carrying one, pick it up. If you run into a grain of sand and you are carrying one, drop it.
This is the sort of thing that nature does - the constraint here is that your ants are pretty stupid - they only have room in their minds for a couple of simple, concrete rules, and they can't even talk to one another. There's no possibility of having a foreman. But even with those constraints, they can still build a pile.