Reticulate tissue systems exist in most multicellular organisms, and the principles underlying the formation of cellular networks have fascinated philosophers, mathematicians, and biologists for centuries. In particular, the beautiful and varied arrangements of vascular tissues in plants have intrigued mankind since antiquity, yet the organizing signals have remained elusive. Plant vascular tissues form systems of interconnected cell files throughout the plant body. Vascular cells are aligned with one another along continuous lines, and vascular tissues differentiate at reproducible positions within organ environments. However, neither the precise path of vascular differentiation nor the exact geometry of vascular networks is fixed or immutable. Several recent advances converge to reconcile the seemingly conflicting predictability and plasticity of vascular tissue patterns. A control mechanism in which an apical-basal flow of signal establishes a basic coordinate system for body axis formation and vascular strand differentiation, and in which a superimposed level of radial organizing cues elaborates cell patterns, would generate a reproducible tissue configuration in the context of an underlying robust, self-organizing structure, and account for the simultaneous regularity and flexibility of vascular tissue patterns.