Stromatolites are examples of an iterative system involving radiate accretive growth of microbial mats, biofilm and/or minerals that result from interaction between intrinsic and extrinsic factors, which progressively shape the final morphology. These interactions can neither be easily described by simple mathematical equations, nor by simple physical laws or chemical reactions. Therefore, a holistic approach that will reduce the system to a set of variables (which are combinations of natural variables) is proposed in order to create virtual morphologies which will be compared with their natural counterparts. The combination of both Diffusion Limited Aggregation (DLA) and cellular automata (CA) allows the exploration of the stromatolite morphological space and a representation of the intrinsic and extrinsic factors responsible for natural stromatolite morphogenesis. The holistic approach provides a translation in simple parameters of (1) the way that energy, nutrients and sedimentary particles reach the active surface of a future build-up, (2) how these elements are distributed and used in order to create morphology, and (3) how simple environmental parameters, such as sedimentation, can disturb morphogenesis. In addition, most Precambrian stromatolite morphologies that are impossible to produce with numerical modeling such as the Kardar-Parisi-Zhang (KPZ) equation can be simulated with the DLA-CA model and this, with a minimum set of variables.