The clade of Myxogastria, commonly described as true or plasmodial slime molds, contains more than 1000 species. During their life cycle many of these slime molds develop extended networks of connected veins, known as unicellular (phanero)plasmodia. Among those, Physarum polycephalum gathered by far the most attention of biologists and physicists. Via oscillating cytoplasmic streams nutrients as well as signaling factors spread through the adaptive plasmodial network. These properties have rendered it not only a model organism for acellular slime molds, but also a model to investigate network dynamics, biological fluiddynamics and food foraging behavior. Here, we studied parameters of plasmodial growth and network development, including chemotactic responses, in three slime mold species: Physarum polycephalum, Badhamia utricularis, and Fuligo septica. We discovered significant variations in chemotaxis, velocity, and oscillatory behavior of plasmodia among and within these species. Interestingly the patterns of the variations also reflect phylogenetic relationships of the species. In contrast to a common notion, phaneroplasmodia of slime molds develop diverse and specifically organized networks by triggers yet to be explored. This work lays the ground for studying more of these organisms to understand basic features of planar network organization and their variations, which evolved as successful solutions of nature.