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