Monte Carlo Physarum Machine: Characteristics of Pattern Formation in Continuous Stochastic Transport Networks

TL;DR

This paper introduces Monte Carlo Physarum Machine, a probabilistic model for reconstructing continuous transport networks from sparse data, demonstrating its effectiveness in modeling biological and cosmological structures.

Contribution

The paper presents MCPM, a novel probabilistic model extending Physarum-inspired network formation, applicable to reconstructing large-scale cosmic web structures from observational data.

Findings

MCPM produces diverse network morphologies called 'polyphorms' from intuitive parameters.

MCPM effectively reconstructs 3D density maps of the Cosmic web from cosmological data.

The model shows potential for various domain-specific network reconstruction tasks.

Abstract

We present Monte Carlo Physarum Machine: a computational model suitable for reconstructing continuous transport networks from sparse 2D and 3D data. MCPM is a probabilistic generalization of Jones's 2010 agent-based model for simulating the growth of Physarum polycephalum slime mold. We compare MCPM to Jones's work on theoretical grounds, and describe a task-specific variant designed for reconstructing the large-scale distribution of gas and dark matter in the Universe known as the Cosmic web. To analyze the new model, we first explore MCPM's self-patterning behavior, showing a wide range of continuous network-like morphologies -- called "polyphorms" -- that the model produces from geometrically intuitive parameters. Applying MCPM to both simulated and observational cosmological datasets, we then evaluate its ability to produce consistent 3D density maps of the Cosmic web. Finally, we examine other possible tasks where MCPM could be useful, along with several examples of fitting to domain-specific data as proofs of concept.