To understand the mechanisms underlying the morphogenesis of multicellular organisms we study the dynamic system of cells (cell multiplication, cell migration, apoptosis); local interactions between cells for understanding the convergence of the system to a stable form that is constantly renewed.and the controls established by the nature of the growth of the organism, and its convergence to a stable form. We must be able to formalize it in a proper metric space a metaphor of cell dynamics to nd conditions (decisions, states) in which operational constraints (such as those induced by the tissue or the use of resources) are always satis ed and therefore in which the system is viable and maintain 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 and to describe a simulation tool to study the morphogenesis of a virtual multicellular organism. We formalize mathematically a model of cell dynamic on the principles of morphological analysis. Morphological analysis and viability theory are the mathematical foundations that motivate this work and this tool will test whether a system generated by morphological equations can maintain its shape and remains "viable" in a given environment.