Physarum polycephalum oscillates. Its cytoplasm streams back and forth at roughly two-minute intervals, driven by peristaltic contractions in its tube network. This oscillation is how it moves and how it "thinks."
In 2008, researchers applied periodic cold events — unfavorable conditions — at hourly intervals. After three exposures, the organism slowed at the expected time even when the event wasn't applied. The rhythm had been entrained. The memory is the oscillation, not something stored in the oscillation.
This simulation shows the entrainment mechanism using a phase-coupled oscillator. The organism's natural phase gradually locks to the stimulus schedule. When stimuli stop, the entrained phase persists briefly, then drifts.
What the simulation can't show: The model implements entrainment as a Kuramoto-style phase coupling — the organism's oscillator is attracted toward the phase it had when stimuli arrived. This captures the behavioral result (anticipatory slowing) but specifies a mechanism that the experimental evidence doesn't determine. The actual Physarum mechanism may involve calcium wave dynamics, membrane potential oscillations, or actomyosin feedback loops. The simulation picks one interpretation and runs it as if it were complete.
The coupling constant κ and decay rate are free parameters. Tuned to match the three-exposure result; any other values would produce different behavior. The real organism's parameter values are not known.
See also: slime (maze-solving via hydraulic feedback — a different Physarum memory mechanism) · entry-417: Nowhere to Put It