Biological objects are often "constructive dynamic systems" whose structures evolve as a consequence of their internal dynamics, which in turn is affected by the overall structure. As very few tools are presently adapted to tackle constructive dynamic systems, they constitute fascinating challenges for modeling/simulation. In cell biology, the secretory process in eukaryotic cells corresponds to this type of system, as it appears to autonomously generate new structures as a result of its molecular dynamics. Here I briefly review the only documented case of a membrane-bounded intracellular compartment whose very existence strictly depends on its continued functioning. Indeed, the Golgi apparatus of the yeast Saccharomyces cerevisiae appears at steady-state as a continuously renewed set of transitory membrane-bounded structures that self-mature, rather than as a permanent entity. On the basis of this case and of recent advances in related molecular studies, a detailed model is proposed, that encompasses the birth of a yeast Golgi element and bridges its molecular and morphogenetic aspects. This model is extended to briefly outline three evolutionary "inventions", from S. cerevisiae to another yeast, Pichia pastoris, on to plant, and on to animal cells: stacking, stabilizing and aggregating the primary Golgi elements.