We introduce Monte Carlo Physarum Machine: a dynamic computational model designed for reconstructing complex transport networks. MCPM extends existing work on agent-based modeling of Physarum polycephalum with a probabilistic formulation, making it suitable for 3D reconstruction and visualization problems. Our motivation is estimating the distribution of the intergalactic medium—the cosmic web , which has so far eluded full spatial mapping. MCPM proves capable of this task, opening up a way towards answering a number of open astrophysical and cosmological questions.