Abstract
The slime mould Physarum polycephalum is known to construct protoplasmic transport networks which approximate proximity graphs by foraging for nutrients during its plasmodial life cycle stage. In these networks, nodes are represented by nutrients and edges are represented by protoplasmic tubes. These networks have been shown to be efficient in terms of length and resilience of the overall network to random damage. However, relatively little research has been performed in the potential for Physarum transport networks to approximate the overall shape of a data-set. In this paper we distinguish between connectivity and shape of a planar point data-set and demonstrate, using scoping experiments with plasmodia of P. polycephalum and a multi-agent model of the organism, how we can generate representations of the external and internal shapes of a set of points. As with proximity graphs formed by P. polycephalum, the behaviour of the plasmodium (real and model) is mediated by environmental stimuli. We further explore potential morphological computation approaches with the multi-agent model, presenting methods which approximate the Convex Hull and the Concave Hull. We demonstrate how a growth parameter in the model can be used to transition between Convex and Concave Hulls. These results suggest novel mechanisms of morphological computation mediated by environmental stimuli.
Highlights
Slime mould Physarum polycephalum is a single-celled organism which is capable of remarkable biological and computational feats, despite possessing no nervous system, skeleton or organised musculature
The study of the computational potential of the Physarum plasmodium was initiated by Nakagaki et al [1] who found that the plasmodium could solve simple maze puzzles
It is known that the growth of P. polycephalum is affected by stimuli within its environment
Summary
Slime mould Physarum polycephalum is a single-celled organism which is capable of remarkable biological and computational feats, despite possessing no nervous system, skeleton or organised musculature. By using a multi-agent model of Physarum which behaves as an adaptive virtual material is is possible to slow the adaptation of the (virtual) plasmodium so that, as it adapts, it retains its solid shape This was used in a simple method so approximate a combinatorial optimisation problem by shrinkage [18]. During this shrinkage process a transition continuum was seen from the complete coverage of the data set (the initial inoculation pattern) down to the Steiner Minimum Tree This suggests the possibility of using morphological adaptation to compute the area occupied by, and the general shape of, a set of points. We begin by assessing the possibility of confining the plasmodium to represent shape using attractants and light illumination We reproduce these results in a multi-agent model and extend the modelling approach to examine different methods of approximating the Convex Hull and the Concave Hull. We devise a parameter which can be used to control the concavity of a growing model plasmodium
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