Here's an interesting example of emergent properties.

In short, it's essentially a topology-based approach to solving a classical optimization problem. Quite novel, really, though it's not clear if the solution offers a whole lot of benefit over brute force calculation in terms of saved computation time. The paper is here.

What struck me as particularly interesting was the authors' proposal to physically implement their "blob" model:

...it would be satisfying if this virtual material could be implemented and embodied in a real physical substrate with the desired physical (for example visco-elastic, free energy minimisation) properties.

What would this accomplish? I'm not saying that it wouldn't be a neat, cheap engineering project to build an elastic blob capable of solving traveling salesman problems, it just doesn't seem like any kind of a job for real-world models.

Jeff Jones, & Andrew Adamatzky (2013). Computation of the Travelling Salesman Problem by a Shrinking Blob arXiv arXiv: 1303.4969v2