Morphogenesis in plants arises from the interplay of genetic and physical interactions within a growing network of cells. The physical aspects of cell proliferation and differentiation are genetically regulated, but constrained by mechanical interactions between the cells. Higher plant tissues consist of an elaborate three-dimensional matrix of active cytoplasm and extracellular matrix, where it is difficult to obtain direct measurements of geometry or cell interactions. To properly understand the workings of plant morphogenesis, it is necessary to have biological systems that allow simple and direct observation of these processes. We have adopted a highly simplified plant system to investigate how cell proliferation and expansion is coordinated during morphogenesis. Coleocheate scutata is a microscopic fresh-water green alga with simple anatomical features that allow for accurate quantification of morphogenetic processes. Image analysis techniques were used to extract precise models for cell geometry and physical parameters for growth. This allowed construction of a deformable finite element model for growth of the whole organism, which incorporated cell biophysical properties, viscous expansion of cell walls, and rules for regulation of cell behavior. The study showed that a simple set of autonomous, cell-based rules are sufficient to account for the morphological and dynamic properties of Coleochaete growth. A variety of morphogenetic behavior emerged from the application of these local rules. Cell shape sensing is sufficient to explain the patterns of cell division during growth. This simplifying principle is likely to have application in modeling and design for engineering of higher plant tissues.