Reticulate leaf venation in Pilea peperomioides is a Voronoi diagram

Reticulate leaf venation, characterized by the presence of loops, is a distinguishing feature of many flowering plants. However, our understanding of both the geometry and the morphogenesis of reticulate vein patterns is far from complete. We show that in the Chinese money plant (Pilea peperomioides), major veins form an approximate Voronoi diagram surrounding secretory pores known as hydathodes. We also propose a mechanistic model based on polar transport of the plant hormone auxin to produce Voronoi patterns, and we support this model with experimental evidence. In contrast to classical models where veins directly connect auxin sources to sinks, our model generates veins that bisect the space between adjacent auxin sources, collectively forming loops. The paradigm change offered by this model may open the door to study reticulate vein formation in other species. Reticulate venation patterns on leaves are ubiquitous in nature yet have eluded characterization. Here the authors report a naturally occurring Voronoi diagram in the plant Pilea peperomioides, and propose a generative algorithm to form this pattern.