Background. Integration of reductionist and holistic approaches is one of the great challenges for mathematical modeling. Mathematical models of complex systems are divided into black-box, white-box and grey-box types. A black-box model is completely nonmechanistic as internal mechanisms of a modeled complex system are hidden. A white-box model demonstrates direct mechanisms of functioning of a complex system. It holistically shows all events at microlevel, mesolevel and macrolevel of a modeled system at all stages of its dynamics. Earlier we have used the white-box modeling for verification and reformulation of the competitive exlusion principle. Here we investigate our white-box model of single-species population dynamics. This is fundamentally important because most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka-Volterra models. Methods. Our white-box model of single-species population growth is a purely logical deterministic individual-based cellular automata model. A biological prototype of the model is a vegetative propagation of rhizomatous lawn grasses. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We also investigate different size and structure of the habitat and two types of fecundity. Results. We have created and investigated a logical white-box model of an ecosystem with one species. This model demonstrates mechanisms of the S-shaped and double S-shaped population growth. We have investigated population growth limited by different factors, in particular by resources, habitat structure, intraspecific competition, lifetime of individuals, regeneration time and fecundity of individuals. We have compared the S-shaped curves with J-shaped curves of population growth. Conclusion. We present a basic white-box model of population dynamics which combines reductionist and holistic approaches. Integration of reductionist and holistic approaches is provided by the simultaneous modeling of both part-whole and cause-effect relations in complex system. We consider this holystic multi-level white-box modeling approach as a method of artificial intelligence which works as hyper-logical automatic deductive inference that provides direct mechanistic insights into complex systems. The white-box modeling by logical deterministic cellular automata is a perspective way for investigation not only of population dynamics but also of any complex systems.