One goal of cell biology is to understand how cells adopt different shapes in response to varying environmental and cellular conditions. Achieving a comprehensive understanding of the relationship between cell shape and environment requires a systems-level understanding of the signalling networks that respond to external cues and regulate the cytoskeleton. Classical biochemical and genetic approaches have identified thousands of individual components that contribute to cell shape, but it remains difficult to predict how cell shape is generated by the activity of these components using bottom-up approaches because of the complex nature of their interactions in space and time. Here, we describe the regulation of cellular shape by signalling systems using a top-down approach. We first exploit the shape diversity generated by systematic RNAi screening and comprehensively define the shape space a migratory cell explores. We suggest a simple Boolean model involving the activation of Rac and Rho GTPases in two compartments to explain the basis for all cell shapes in the dataset. Critically, we also generate a probabilistic graphical model to show how cells explore this space in a deterministic, rather than a stochastic, fashion. We validate the predictions made by our model using live-cell imaging. Our work explains how cross-talk between Rho and Rac can generate different cell shapes, and thus morphological heterogeneity, in genetically identical populations.