Abstract
The single-celled organism Physarum polycephalum efficiently constructs and minimises dynamical nutrient transport networks resembling proximity graphs in the Toussaint hierarchy. We present a particle model which collectively approximates the behaviour of Physarum. We demonstrate spontaneous transport network formation and complex network evolution using the model and show that the model collectively exhibits quasi-physical emergent properties, allowing it to be considered as a virtual computing material. This material is used as an unconventional method to approximate spatially represented geometry problems by representing network nodes as nutrient sources. We demonstrate three different methods for the construction, evolution and minimisation of Physarum-like transport networks which approximate Steiner trees, relative neighbourhood graphs, convex hulls and concave hulls. We extend the model to adapt population size in response to nutrient availability and show how network evolution is dependent on relative node position (specifically inter-node angle), sensor scaling and nutrient concentration. We track network evolution using a real-time method to record transport network topology in response to global differences in nutrient concentration. We show how Steiner nodes are utilised at low nutrient concentrations whereas direct connections to nutrients are favoured when nutrient concentration is high. The results suggest that the foraging and minimising behaviour of Physarum-like transport networks reflect complex interplay between nutrient concentration, nutrient location, maximising foraging area coverage and minimising transport distance. The properties and behaviour of the synthetic virtual plasmodium may be useful in future physical instances of distributed unconventional computing devices, and may also provide clues to the generation of emergent computation behaviour by Physarum.
Highlights
The single-celled multinucleate myxomycete organism Physarum polycephalum has been the subject of recent research interest because the transport networks formed during its growth and adaptation to the environment exhibit complex patterning and adaptive, distributed behaviour
We have presented a particle model whose interactions produce complex emergent behaviour resulting in a synthetic virtual material which approximates the network formation and evolution of the plasmodium of Physarum polycephalum
We analysed the evolution of the emergent transport networks around food sources and found that food position were critical in guiding network evolution
Summary
The single-celled multinucleate myxomycete organism Physarum polycephalum has been the subject of recent research interest because the transport networks formed during its growth and adaptation to the environment exhibit complex patterning and adaptive, distributed behaviour. In this paper we present a population based particle model of Physarum which collectively approximates the complex formation and evolution of transport networks seen in the organism. We study the properties of, and influences upon, the synthetic emergent transport networks and describe methods in which the particle population may, like Physarum, be considered as a (virtual) substrate for spatially represented computing tasks. We present a simple particle population model of Physarum which approximates the complex network formation and evolution seen in the plasmodium.
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