From simplicity, complexity. That is the underlying principle of emergent behaviour. It is also the motto of parliament, but that's by the by.
A large part of my DPhil is likely to be focussed upon that most zoological of emergent behaviours, collective motion. Many different statistical properties of biological collective motion have been observed, including so-called 'giant-number fluctuations' in which the density of individuals at a given point fluctuate wildly, and power-law distributions of group sizes within a population. A remarkable facet of collective motility is that these properties appear to be similar at all scales, from bacillus to buffalo.
One of the earliest modelling approaches of collective motion to demonstrate interesting emergent behaviour was discussed in Vicsek et al 1995. Particles in this model (animals or cells, depending on your point of view) take on the average orientation of their neighbors. Although the model is extremely simple, the statistical behaviour that emerges looks strikingly similar to many natural flocking patterns.
I have written a Matlab implementation of this model, an example simulation of which can be seen below. The code for these simulations (or at least ones like it) can be downloaded here. To use it, simply run the script RunModel.m in Matlab. Resulting movies can then be viewed with the command movie(Frames).
Oh, and I should point out that I will not actually be looking at bacillus flagellar motility in my research, as the title of this section suggests. It just would have been remiss of me to let relevance stand in the way of a bad pun.