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Plasmodium of true slime mold, Physarum polycephalum, is an amoeba-like unicellular organism. It crawls in environment with oscillating the cell thickness. The oscillating parts of the plasmodium are connected through tube structures where the protoplasm (intracellular substance) streams. Thus the plasmodium can be modeled as a network consisting of oscillating nodes (or vertices) and links (or edges). In this paper, the network geometries in various environments were analyzed with considering the relation with the spatio-temporal oscillating pattern in the each network. We show the geometry of the networks depends on environmental condition:It forms lattice networks in pleasant environment, tree-graph networks in unpleasant environment, and intermixture of them in neutral environment. The relation between the morphology and the biological function of the plasmodia is discussed in the context of spatio-temporal structure.

Morphology and Biological Function-Spatio-temporal Structure in an Oscillating Amoeboid Unicellular Organism of True Slime Mold-