The experimental data represented in the bibliography are theoretically analyzed to construct an adequate model for dynamics of an open nonequilibrium living system. It is shown that the viable microorganisms are capable of forming the fractal structure, whose dimensionality is certainly non-integral. In addition, we have attempted to provide a generalized description of the properties of living and nonliving matter (in the addition to that described in work [1]). Relevant published data were used to demonstrate a fractal structure of the space in the vicinity of centrally gravitating bodies with satellites revolving around them along closed trajectories and serving as a kind of testers of the neighboring space. A local violation of its discontinuity is likely to be a necessary (yet not sufficient!) dynamic characteristic of the spatiotemporal continuum for self-organization of molecules into a living, i.e., self-replicating, system.