Formation of trails and exploration networks by ants
Many ant species produce large dendritic networks of trails around their nest. It has been suggested that the form of the trail network somehow provides an optimal solution to reach different points around the nest.
It was also suggested that the angles between different branches provide cues that are used by some ant species to orient themselves. 
In fact different authors report that in the trail networks of most species, the two children branches following a bifurcation form an angle of about 60 degrees. It is not known which mechanisms lead to the formation of angles with this value.
When a colony of Argentine ants (Linepithema humile) is given access to a circular arena, it is possible to observe the formation of one such network in controlled experimental conditions (see the image on the right, showing the evolution of the trail network over one hour from the beginning of the experiment; ants enter the arena from the centre).
The formation of ant trails results from feedback mechanisms that involve the use of pheromones: pheromones are chemicals that attract other ants. Argentine ants use pheromones to mark their path when they explore the environment in search of food. These in turn attract more ants to walk in the same direction and the new ants will reinforce the trail. In the end a network is formed.
When in Toulouse, I collected a large amount of data on the formation of trail networks with this setup. The basic idea is try to understand how the final form of the network and its evolution over time result from the individual displacement of ants. In particular, ants are considered active random walkers whose probability to move in a particular direction is determined by the concentration of pheromone on neighbouring points in the arena, but the map of pheromone is in turn changed by the passage of ants.
Ant exploratory patterns present some similarities to other naturally occurring patterns of physical origin as dielectric breakdown patterns (example on the left taken from Niemeyer et al. 1984)
Studying the formation of these patterns in ant colonies offers the advantage that the exact behaviour of all individual ants can be observed experimentally as well as the global pattern.