  The giant single-celled slime mould Physarum polycephalum has inspired rapid
develop- ments in unconventional computing substrates since the start of this
century. This is primarily due to its simple component parts and the
distributed nature of the computation which it approximates during its growth,
foraging and adaptation to a changing environment. Slime mould functions as a
living embodied computational material which can be influenced (or pro-
grammed) by the placement of external stimuli. The goal of exploiting this
material behaviour for unconventional computation led to the development of a
multi-agent approach to the ap- proximation of slime mould behaviour. The basis
of the model is a simple dynamical pattern formation mechanism which exhibits
self-organised formation and subsequent adaptation of collective transport
networks. The system exhibits emergent properties such as relaxation and
minimisation and it can be considered as a virtual computing material,
influenced by the external application of spatial concentration gradients. In
this paper we give an overview of this multi-agent approach to unconventional
computing. We describe its computational mechanisms and different generic
application domains, together with concrete example ap- plications of material
computation. We examine the potential exploitation of the approach for
computational geometry, path planning, combinatorial optimisation, data
smoothing and statistical applications.
