Physarum computing and topology optimisation

The plasmodium stage of the giant single-celled amoeboid organism Physarum polycephalum, or true slime mould, dynamically adapts its body plan in response to environmental stimuli, including nutrient location, temperature gradients, light exposure, and predatory threats. The construction and adaptation of the plasmodial transport network has been shown to be an efficient trade-off between minimising network distance and maximising connectivity. Optimisation of topology is also a desired trait in manufacturing and engineering, whereby the topology of an initially simple component is modified to minimise one or more properties (for example minimising the amount of substrate reduces the weight and material cost of the component) whilst maintaining other desired material properties within the component (for example strength under specific load points and conditions). Biologically inspired approaches to certain specific engineering challenges are well documented and successful. In this paper we explore at a more general level whether a cross-pollination can occur between Physarum computing and Topology Optimisation. Using an interdisciplinary modelling approach we explore whether the evolution of transport networks in a multi-agent model of Physarum has any similarities to networks formed by Topology Optimisation. We find that the Topology Optimisation method generates networks which are similar to the model slime mould networks. The Topology Optimisation networks correspond to higher regions of the Toussaint hierarchy of proximity graphs (i.e. more edges) whereas the model slime mould networks exhibit greater minimisation of network length. Since it is possible to adjust network connectivity in the multi-agent model via nutrient concentration we speculate that similar parametric adjustment may be possible to alter the connectivity of Topology Optimisation networks.