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The treelike structures of many organs, including the mammary gland, are generated by branching morphogenesis, a reiterative process of branch initiation and invasion from a preexisting epithelium. Using a micropatterning approach to control the initial three-dimensional structure of mouse mammary epithelial tubules in culture, combined with an algorithm to quantify the extent of branching, we found that the geometry of tubules dictates the position of branches. We predicted numerically and confirm experimentally that branches initiate at sites with a local minimum in the concentration of autocrine inhibitory morphogens, such as transforming growth factor–β. These results reveal that tissue geometry can control organ morphogenesis by defining the local cellular microenvironment, a finding that has relevance to control of invasion and metastasis.