Pluripotent embryonic stem cells (ESCs) can differentiate into all somatic cell types, making them a useful platform for studying a variety of cellular phenomenon. Furthermore, ESCs can be induced to form aggregates called embryoid bodies (EBs) which recapitulate the dynamics of development and morphogenesis. However, many different factors such as gradients of soluble morphogens, direct cell-to-cell signaling, and cell-matrix interactions have all been implicated in directing ESC differentiation. Though the effects of individual factors have often been investigated independently, the inherent difficulty in assaying combinatorial effects has made it difficult to ascertain the concerted effects of different environmental parameters, particularly due to the spatial and temporal dynamics associated with such cues. Dynamic computational models of ESC differentiation can provide powerful insight into how different cues function in combination both spatially and temporally. By combining particle based diffusion models, cellular agent based approaches, and physical models of morphogenesis, a multi-scale, rules-based modeling framework can provide insight into how each component contributes to differentiation. I propose to investigate the complex regulatory cues which govern complex morphogenic behavior in 3D ESC systems via a computational rules based modeling approach. The objective of this study is to examine how spatial patterns of differentiation by ESCs arise as a function of the microenvironment. The central hypothesis is that spatial control of soluble morphogens and cell-cell signaling will allow enhanced control over the patterns and efficiency of stem cell differentiation in embryoid bodies.