[Paper Review] Slime Mould Inspired Generalised Voronoi Diagrams with Repulsive Fields

Jeff Jones, Andrew Adamatzky|arXiv (Cornell University)|Mar 24, 2015

Slime Mold and Myxomycetes Research8 references3 citations

TL;DR

This paper proposes a novel computational model inspired by the slime mould Physarum polycephalum that generates generalized Voronoi diagrams using both attractive and repulsive stimuli. By simulating plasmodial growth toward attractants and avoidance of repellents, the model approximates Voronoi diagrams for point sources, complex shapes, and circular sets, demonstrating that repulsive fields maintain spatial partitioning while minimizing internal network connectivity.

ABSTRACT

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.

Motivation & Objective

• To explore how repulsive fields influence the formation of Voronoi diagrams in unconventional computing systems.
• To investigate whether Physarum polycephalum's behavior can be abstracted into a computational model that generalizes Voronoi diagram construction.
• To demonstrate the approximation of Voronoi diagrams using combined attraction and repulsion stimuli in various geometric configurations.
• To analyze how repellent concentration affects network connectivity while preserving spatial partitioning.
• To extend the repertoire of unconventional computation by incorporating repulsive stimuli as a computational primitive.

Proposed method

• Modeling Physarum as a distributed virtual computing material with uniform propagation of information via fronts from source nodes.
• Simulating plasmodial growth toward attractant sources and avoidance of repellent sources using a reaction-diffusion-like mechanism.
• Representing Voronoi bisectors as regions where plasmodial fronts meet or where vacant zones form before fusion.
• Using a computational framework to simulate the contraction and expansion dynamics of protoplasmic tubes under dual stimuli.
• Applying the model to generate Voronoi diagrams for point sets, complex planar shapes, and circular sets.
• Varying repellent concentration to study its effect on network connectivity and spatial partitioning.

Experimental results

Research questions

• RQ1 Can a Physarum-inspired model approximate generalized Voronoi diagrams using both attractants and repellents?
• RQ2 How does the inclusion of repulsive fields affect the topology and connectivity of the resulting transport network?
• RQ3 What is the relationship between repellent concentration and the preservation of spatial partitioning in the Voronoi diagram?
• RQ4 Can the model generate accurate Voronoi diagrams for non-point sources such as complex shapes and circles?
• RQ5 How do combined attraction and repulsion stimuli influence the emergence of stable Voronoi structures?

Key findings

• The model successfully approximates Voronoi diagrams for point data sources, complex planar shapes, and circular sets using combined attraction and repulsion.
• Repellent fields maintain spatial partitioning between generating points while minimizing internal network connectivity through contractile forces.
• The system demonstrates robustness in generating Voronoi bisectors via two distinct mechanisms: front collision and vacant region formation.
• Varying repellent concentration allows control over network connectivity without disrupting the overall spatial partitioning.
• The addition of repulsive stimuli enhances the computational repertoire of unconventional systems, enabling new approaches to plane-division and minimization problems.
• The model confirms that Physarum’s natural behavior can be abstracted into a general-purpose computational framework for spatial computation.