  The Travelling Salesman Problem (TSP) is a well known and challenging
combinatorial optimisation problem. Its computational intractability has
attracted a number of heuristic approaches to generate satisfactory, if not
optimal, candidate solutions. In this paper we demonstrate a simple
unconventional computation method to approximate the Euclidean TSP using a
virtual material approach. The morphological adaptation behaviour of the
material emerges from the low-level interactions of a population of particles
moving within a diffusive lattice. A `blob' of this material is placed over a
set of data points projected into the lattice, representing TSP city locations,
and the blob is reduced in size over time. As the blob shrinks it
morphologically adapts to the configuration of the cities. The shrinkage
process automatically stops when the blob no longer completely covers all
cities. By manually tracing the perimeter of the blob a path between cities is
elicited corresponding to a TSP tour. Over 6 runs on 20 randomly generated
datasets of 20 cities this simple and unguided method found tours with a mean
best tour length of 1.04, mean average tour length of 1.07 and mean worst tour
length of 1.09 when expressed as a fraction of the minimal tour computed by an
exact TSP solver. We examine the insertion mechanism by which the blob
constructs a tour, note some properties and limitations of its performance, and
discuss the relationship between the blob TSP and proximity graphs which group
points on the plane. The method is notable for its simplicity and the spatially
represented mechanical mode of its operation. We discuss similarities between
this method and previously suggested models of human performance on the TSP and
suggest possibilities for further improvement.
