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Aggregates of stem cells can break symmetry and self-organize into embryo-like structures with complex morphologies and gene expression patterns. Mechanisms including reaction-diffusion Turing patterns and cell sorting have been proposed to explain symmetry breaking but distinguishing between these candidate mechanisms of self-organization requires identifying which early asymmetries evolve into subsequent tissue patterns and cell fates. Here we use synthetic ‘signal-recording’ gene circuits to trace the evolution of signalling patterns in gastruloids, three-dimensional stem cell aggregates that form an anterior–posterior axis and structures resembling the mammalian primitive streak and tailbud. We find that cell sorting rearranges patchy domains of Wnt activity into a single pole that defines the gastruloid anterior–posterior axis. We also trace the emergence of Wnt domains to earlier heterogeneity in Nodal activity even before Wnt activity is detectable. Our study defines a mechanism through which aggregates of stem cells can form a patterning axis even in the absence of external spatial cues.