Senior Lecturer in Theoretical Biology


Life Sciences
Roehampton University
London SW15 5PJ


andrea.perna at

The arboreal nests of Nasutitermes termites

The structure that you see below is a small fragment of termite nest, built by the Australian species Nasutitermes walkeri. Unlike the nest built by other species, these Nasutitermes nests present an apparently "chaotic" organisation, with new galleries that branch and open in every direction forming a large and complex maze. We don't know exactly how thousands of termites coordinate their activities to build such structures, but we know that much of the coordination between workers is mediated through the building substrate itself: each individual senses the local configuration of the nest and responds to it by depositing or removing a new pellet. This is a general coordination mechanism known as stygmergy.

fragment of Nasutitermes walkeri termite nest

An architecture of negative curvature

Observing these Nasutitermes nests at the small scale, we notice that a large number of walls are arranged in a saddle-shaped configuration. Surfaces like these are usually called surfaces with negative Gaussian curvature, which expresses the fact that if you focus on a point on the surface, the two principal curvatures (in red and in grey) bend in opposite directions.
Structures with negative curvature are relatively rare in human architecture, but they have a number of very interesting properties and include many “minimal surface”, such as the gyroid, which are known to offer good mechanical resistance for little weight.

Negative curvature

A simple building rule

One of our hypotheses is that the local curvature of the surface is the main stigmergic stimulus that modulates the behaviour of termites: termites would have a high tendency to deposit new pellets wherever there is a region with high curvature, an unfinished wall, an edge, a pillar, while at the same time smoothing out smaller asperities.
Termites interact primarily with the substrate -rather than with other termites- when deciding where to add new pellets. In addition, the high density of worker termites inside the nest means that construction is not limited by the availability of workers. Because of this, we can almost ignore the behaviour of individual termites: we can model nest construction as a wall that grows by itself based on its local curvature!

curvature-based growth of pillars and walls

The wall grows preferentially where its curvature is high, at the tip; if the tip also flattens while growing, the maximum of curvature is displaced to the sides of the tip and branching occurs. In three dimensions, a wall will branch to form a Y-shaped cylindre, whereas a pillar will produce a conical surface, that might later destabilise into several pillars.

Explore the structure in three dimensions

In the images below you can visualise a small fragment of Nasutitermes nests (on the left) and a gyroid (on the right).

Related scientific publications