From the animal blood circulatory systems to the plant xylem and phloem, distribution networks deliver load and remove waste, while adapting to competing evolutionary pressures. We are interested in understanding the evolutionary pressures behind the complex reticulate architectures we frequently observe in a variety of systems.

Such systems include: insect wings, gorgonian corals, the developing vasculature of the retina, lowland river networks and the arterial vasculature of the mamalian neocortex. Leaves provide an excellent testbed for the development of ideas that could apply to reticulate webs such as these. 
Leaves are endowed with a complex network of veins that ensures that they stay properly hydrated and photosynthetically functional. Leaf vein architecture has evolved from the primitive, dichotomous venation of ancient ferns and progymnosperms to the hierarchical, reticulate venation of modern angiosperm plants. We want to understand the physical principles and functional requirements that have driven the evolution of modern, loopy venation patterns.
Gingko and lemon leaves. Fruorescent dye tracing experiments. The treelike architecture of the ancient Ginkgo vasculature does not allow for rerouting of the flow around an injury site. The modern dicot lemon leaf is reticulate allows for efficient rerouting of the flow.

What is the architecture of an optimal biological distribution network? Through large scale computer simulations we find the topology of the leaf (and other) vein networks that optimize a series of prescribed functional demands that are physiologically relevant. Comparing the results of the simulations with real data we can infer the possible functional pressures that drive the evolution of different plant taxa and compare with ecological and phylogenetic evidence. 
To perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring reticulate graphs we need robust metrics. We develop new metrics based on an algorithm that maps the connectivity of loopy networks to binary trees. We use these metrics to investigate computer generated and natural graphs and to extract subtle information about the topology of the networks and decipher their structure. 


How do curved structures fold? How could one design origami with paper that is not intrinsically flat? Inspired by the natural folding of pollen grains, a biological process of high importance, we investigate how simple geometrical and mechanical design principles determine the folding pathways of structures with nonzero intrinsic curvature. 