YOU’RE SO VEIN: Beauty and Utility in a Leaf. You may have marveled at the intricate veins on a leaf, but did you know that the same pattern appears all over nature? The recursive looped network is found in neural nets, river deltas, insect wings and capillaries overlying a tumor.
• Inspired by leaf venation, mathematical physicists Marcelo Magnasco and Eleni Katifori of Rockefeller University wondered if there was an evolutionary basis for the selection of high density loops in networks. They digitally dissected the pattern and used complex algorithms to derive optimal solutions for two challenges facing any transport network: resilience to damage and fluctuations in load.
• The animated gif shows how flow of a fluorescent dye is routed around an injury (circular hole) in the main vein of a leaf, via closed loops, to reach the leaf tip. If the network had a simple tree-like branching pattern as is commonly assumed, then damage to any vein would result in tissue death downstream. Instead, the leaf is remarkably resilient to damage by insects, pathogens and the elements.
• Variations in load are also handled best by recursively nested loops. Some parts of the leaf may be lit by sunlight and exert greater demands on flow compared to shady parts. Again, hierarchically ordered trees are not as effective as topologically disordered networks seen in leaf vasculature. It took a unique partnership of physics and biology to reveal that Nature is a Master Engineer!
★★★ Many thanks to Kevin Staff for donating his time and skills in making the gif for ScienceSunday !
Watch: Lighting up Leaves
REF: Damage and Fluctuations Induce Loops in Optimal Transport Networks Eleni Katifori, Gergely J. Szollosi, and Marcelo O. Magnasco