Loopy leaf veins

Unlike the branches of a tree, the network of veins in a typical leaf is full of closed loops. Even after a visit by a hungry insect, no part of the leaf is cut off from the network, as shown in the top part of the figure. But is a leaf’s fractal-like form, with loops of various sizes, the best possible network for resisting that type of damage, or might a different loop-filled structure be better? And is the hierarchical structure the optimum for any other criterion? Marcelo Magnasco (the Rockefeller University, New York) and colleagues sought to find out. Using a mathematical model that assigns each vein segment a cost proportional to its capacity raised to a power γ, they looked for the networks with a given total cost that suffered the least average strain under two sets of circumstances. First, they looked at damage to a randomly chosen...