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 vein segment. Second, they considered the case of a fluctuating load, in which the amount of fluid to be delivered to each part of the network varied in time and space. (Real leaves do sometimes need to handle fluctuating loads. So, more obviously, do most human-built networks.) They found that for low values of γ (results for γ = 0.1 are shown in the figure), both cases yielded hierarchical networks of loops, qualitatively similar to real leaves. (E. Katifori, G. J. Szöllősi, M. O. Magnasco, Phys. Rev. Lett. 104 , 048704, 2010 http://dx.doi.org/10.1103/PhysRevLett.104.048704 .)