  The giant single-celled amoeboid organism Physarum polycephalum constructs
minimising transport networks but can also approximate the Voronoi diagram
using two different mechanisms. In the first method Voronoi bisectors are rep-
resented by deformation of a pre-existing plasmodial network by repellent
sources acting as generating points. In the second method generating points act
as inoculation sites for grow- ing plasmodia and Voronoi bisectors are
represented by vacant regions before the plasmodia fuse. To explore the
behaviour of minimising networks in the presence of repulsion fields we utilise
a computational model of Physarum as a distributed virtual computing material.
We characterise the different types of computational behaviours elicited by
attraction and repulsion stimuli and demonstrate the approximation Voronoi
diagrams using growth towards attractants, avoidance of repellents, and
combinations of both. Approximation of Voronoi diagrams for point data sources,
complex planar shapes and circle sets is demonstrated. By altering repellent
con- centration we found that partition of data sources was maintained but the
internal network connectivity was minimised by the contractile force of the
transport network. To conclude, we find that the repertoire of unconventional
computation methods is enhanced by the addition of stimuli presented by
repellent fields, suggesting novel approaches to plane-division, packing, and
minimisation problems.
