Slime Mould Inspired Generalised Voronoi Diagrams with Repulsive Fields

The Voronoi diagram is a widely used partition of space which may be implemented in a variety of unconventional computing prototypes, sharing in common the uniform propagation of information via fronts emanating from data point sources. 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 represented 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 growing 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 concentration 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.