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

Abstract

We present Monte Carlo Physarum Machine (MCPM): 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 data sets, 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.

SDSS DR17: The Cosmic Slime Value Added Catalog

“…field estimate of the large-scale structure spanning 37.6k SDSS galaxies within the 0.018 < z < 0.038 range. The detailed description of methodology and analyses are described in Elek et al (2022). We provide a brief summary of the model here.…”

“…This section describes how we calibrate the MCPM algorithm using the Bolshoi-Planck data. We refer readers to Elek et al (2022) for more details of the fitting procedure and the impact of the model hyperparameters on the resulting reconstruction geometry. Readers interested in the catalog data can skip to Section 3.3.…”

“…In Figure 4, we demonstrate that MCPM reconstructs not just the halos that we feed into it but the cosmic structure, including filaments and voids. More quantitative assessments are available in Elek et al (2022).…”

“…In this manuscript, we employ the novel method first introduced in Burchett et al ( 2020) described in detail by Elek et al (2022), which is based on the morphology of the Physarum polycephalum slime mold organism to map the cosmic density field. This model implicitly traces the cosmic web structure by efficiently finding optimal pathways between the galaxies that trace filaments.…”

The Evolving Effect of Cosmic Web Environment on Galaxy Quenching

“…There are several other cosmic web reconstruction techniques that have been employed for cosmic web studies, which have advantages and disadvantages over the DISPERSE framework (see Libeskind et al 2018 for a detailed comparison of many of these methods). We are currently applying a new state-of-theart cosmic web reconstruction algorithm called the Monte Carlo Physarum Machine (MCPM), inspired by the Physarum polycephalum (slime mold) organism (Elek et al 2021(Elek et al , 2022, to compare to the local density estimation and global cosmic web characterization from DISPERSE. This method produces continuous cosmic matter densities (as opposed to discrete DTFE densities at the locations of galaxies) and has been applied successfully to both theoretical and observational data sets (e.g., Burchett et al 2020;Simha et al 2020;Wilde et al 2023).…”