In biology, recent techniques in confocal mi- croscopy have produced experimental data which highlights the importance of cellular dynamics in the evolution of biolog- ical shapes. Thus, to understand the mechanisms underlying the morphogenesis of multi-cellular organisms, we study this cellular dynamic system in terms of its properties: cell multi- plication, cell migration, and apoptosis. Besides, understanding the convergence of the system toward a stable form, involves local interactions between cells. Indeed, the way that cells self- organize through these interactions determines the resulting form. Along with the mechanisms of convergence highlighted above, the dynamic system also undergoes controls established by the nature on the organisms growth. Hence, to let the system viable, the global behavior of cells has to be assessed at every state of their developement and must satisfy the constraints. Otherwise, the whole system self-adapts in regard to its global behavior. Thus, we must be able to formalize in a proper metric space a metaphor of cell dynamics in order to find conditions (decisions, states) that would make cells to self-organize and in which cells self-adapt so as to always satisfy operational constraints (such as those induced by the tissue or the use of resources). Therefore, the main point remains to find conditions in which the system is viable and maintains its shape while renewing. The aim of this paper is to explain the mathematical foundations of this work and describe a simulation tool to study the morphogenesis of a virtual organism.