Constraints of space in plant development.

Like all forms in nature, plants are subject to the properties of space. On the one hand, space prevents configurations that would place more than one component in the same location at the same time. A generalization of this constraint limits proximity and density of organs. On the other hand, space provides a means for a plant to create three-dimensional forms by differentially controlling their growth. This results from a connection between the metric properties of surfaces and their Gaussian curvature. Three strategies used by plants to develop within the constraints of space are presented: expansion to another dimension, egalitarian partitioning of space, and competition for space. These strategies are illustrated with examples of curved surfaces of leaves and petals, self-similar branching structures of compound leaves and inflorescences, and tree architecture. The examples highlight the fundamental role of the constraints of space in plant development, and the complementary role of genetic regulation and space-dependent emergent phenomena in shaping a plant.