State-Modulated Monte Carlo Physarum Machine for Energy-Constrained Collective Navigation
While I was developing Plasmodia game, I started by using Jeff Jones' algorithm of physarum behaviour, but the game needed more survival and environmental variables, so I started adding those to the code. At some point I asked myself is this still Jones' algorithm or is it a new version. I took a two week break from the development and wrote this paper.
Abstract: We present SM-MCPM (State-Modulated Monte Carlo Physarum Machine), an extension of physarum-based collective algorithms incorporating behavioral state machines and metabolic constraints. Classical physarum models treat agents as memoryless particles whose behavior depends solely on local pheromone gradients. SM-MCPM agents maintain internal states-Scouting, Returning, LowEnergy, Recharging-that dynamically modulate sensing weights and movement priorities. Agents operate under energy constraints, requiring intermediate recharge stations (nodes) to complete round-trip journeys between a home base (core) and target locations (objectives). The framework produces emergent infrastructure: high-traffic routes consolidate into persistent vein highways providing speed and efficiency bonuses. We formalize the complete system dynamics including the agent state machine, multi-layer sensing model, energy mechanics, and vein formation process. Simulation experiments (N = 100) demonstrate that state modulation is strictly necessary for survival, with the full model achieving 10,277 ± 7,074 round trips compared to zero for a memoryless baseline. Furthermore, we observe emergent range extension, where vein infrastructure allows agents to survive theoretically impossible journeys by reducing metabolic costs. However, this mechanism exhibits high instability (611±707 trips without pre-placed nodes) with a heavy-tailed distribution of outcomes, confirming that reliable collective navigation requires deliberate infrastructure.