When placed at the perimeter of a maze with food in the center, the plasmodial slime mold Physarum polycephalum explores the maze, retracts branches from dead-end corridors, and then grows exclusively along the shortest path possible to the food. How does Physarum do this? One theory is that it leaves behind slime deposits—an externalized 'memory' that 'reminds' it not to retry dead ends.
Physarum is a plasmodial slime mold, whereas Dictyostelum is a cellular slime mold. Compare and contrast movement by the migrating slug stage of Dictyostelium to the plasmodial stage of Physarum.
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Master Excavata and Archaeplastida (Plantae) with a bite sized video explanation from Jason Amores Sumpter