As multicellular organisms grow, positional information is continually needed to regulate the pattern in which cells are arranged. In the Arabidopsis root, most cell types are organized in a radially symmetric pattern; however, a symmetry-breaking event generates bisymmetric auxin and cytokinin signaling domains in the stele. Bidirectional cross-talk between the stele and the surrounding tissues involving a mobile transcription factor, SHORT ROOT (SHR), and mobile microRNA species also determines vascular pattern, but it is currently unclear how these signals integrate. We use a multicellular model to determine a minimal set of components necessary for maintaining a stable vascular pattern. Simulations perturbing the signaling network show that, in addition to the mutually inhibitory interaction between auxin and cytokinin, signaling through SHR, microRNA165/6, and PHABULOSA is required to maintain a stable bisymmetric pattern. We have verified this prediction by observing loss of bisymmetry in shr mutants. The model reveals the importance of several features of the network, namely the mutual degradation of microRNA165/6 and PHABULOSA and the existence of an additional negative regulator of cytokinin signaling. These components form a plausible mechanism capable of patterning vascular tissues in the absence of positional inputs provided by the transport of hormones from the shoot.