Examine the delicate branching patterns on a leaf or a dragonfly’s wing and you’ll see a complex network of nested loops. This pattern can be found scattered throughout nature and structural engineering: in the brain’s cerebral vasculature, arrays of fungi living underground, the convoluted shape of a foraging slime mold and the metal bracings of the Eiffel Tower.
Loop architectures, like redundant computer networks or electrical grids, make structures resistant to damage. As Marcelo Magnasco, a physicist at Rockefeller University, points out, the Eiffel Tower is a clear example of loop construction, designed to maximize the distribution of strain across its recursive frame. But for all the natural examples of loop design, surprisingly little is known about why the networks in leaves and the cortical blood vessels are organized in this way.
“We understand the physics of the connections between entities in full, disgusting detail,” Magnasco said of simple circulatory systems. “Nevertheless, we do not understand the pattern as a whole. We don’t know why they look this way or why every tree is different.”
The Eiffel Tower incorporates many nested loops, designed to distribute strain over the structure.
Image: Courtesy of Quanta magazine
Over the past few years, Magnasco and others have begun to explore exactly why these patterns are so commonly found in nature. Studies on leaves and the brain’s vascular system have confirmed that nested loops provide a structure that is resistant to damage and that can efficiently deal with fluctuations in fluid flow. Now scientists are beginning to quantify the properties of these networks, gaining insight into their essential characteristics, such as resilience, and allowing for more informative comparisons between networks.
“Plants are a spectacular system to work on as physicist, because they are beautifully mathematical,” said Eleni Katifori, a physicist at the Max Planck Institute for Dynamics and Self-Organization, in Göttingen, Germany, who collaborates with Magnasco. Plants grow iteratively and frequently exhibit crystal-like patterns, such as the ones we see in pine cones and sunflowers, she said. “The hope is that if we understand the architecture of veins, we will get a better handle on photosynthetic efficiency in plants.”
Understanding leaf veins may also shed light on the vastly more complex vascular network on the surface of the brain, illuminating the close link between brain activity and blood flow. That relationship, while still poorly understood, provides the foundation for functional magnetic resonance imaging, one of the most popular brain imaging technologies in use today.