Dictyostelium discoideum is a social amoeba exhibiting distinct self-organizing behavior at different phases of its life - moving in a coordinated way towards areas with food, signaling lack of food and recruiting partners to create a single super-organism (fruiting body). These phases and their underlying mechanisms are excellent models useful for understanding other natural cells' behavior (e.g. cancer cells), as well as to engineer artificial systems such as swarms of robots. This paper focuses specifically on the aggregation phase of Dictyostelium discoideum. We present a detailed agent-based - “bottom-up” - model, which exhibits a series of individual, collective behaviors and emergent properties of social amoeba Dictyostelium discoideum. We extended previous models of the aggregation phase with: a pre- aggregation phase; and three different levels of quorum sensing allowing collective decisions to be taken in a decentralized manner for (1) identifying the time for aggregation phase; (2) providing aggregation territories of homogeneous size; (3) allowing the appearance of late centres. The key and unique character of our model is the cells' self-assessment and self-generated gradients arising from six chemical factors: PSF, CMF, Adenosine, cAMP, PDE and CF released by each individual amoeba. We programmed our model in Matlab. Our results show a series of behavior close to the individual and collective behavior of living Dictyostelium discoideum. In particular, we observed: inhibition of centers too close to each other; the appearance of late centers when aggregation territories are too large; and measured homogeneous size aggregation territories emerging from the cells' behavior. Future work will address the remaining phases of the Dictyostelium discoideum life cycle (migration and culmination).