The surface area of a limb, not its thickness, determines how it branches.
When it came to trees, Leonardo da Vinci was completely wrong.
Over 500 years ago, the multitalented Renaissance genius drew down his “law of trees.” It described how he perceived trees to branch. Leonardo’s rule breaks down for many sorts of trees, while being a wonderful insight that enabled him sketch realistic landscapes. Researchers explain in an article released April 13 in Physical Review E that a new branching rule termed “Leonardo-like” works for nearly any leafy tree.
According to physicist Sergey Grigoriev of the Petersburg Nuclear Physics Institute in Gatchina, Russia, “the older Leonardo rule indicates the thickness of the branches, but the length of the branch was not taken into account.” “As a result, the older rule’s description is incomplete.”
The thickness of a limb before it branches into smaller ones is the same as the cumulative thickness of the limbs emerging from it, according to Leonardo’s rule . However, according to Grigoriev and his colleagues, the surface area remains constant.The new rule integrates limb widths and lengths, and predicts that long branches will be thinner than short ones, using surface area as a guide. The new rule, unlike Leonardo’s prediction, works for both slim birches and robust oaks, according to the study.
According to the researchers, the relationship between branch surface area and overall tree structure demonstrates that tree construction is guided by the live outer layers. “As if the tree were a two-dimensional entity,” the authors write in their paper, “the life of a tree flows according to the laws of conservation of area in two-dimensional space.” In other words, it’s as if any tree’s structure is determined solely by two dimensions: the breadth of each limb and the distance between its branchings. As a result, the new rule depicts trees particularly effectively when they are depicted in two dimensions in a painting or on a screen.
According to Katherine McCulloh, a botanist at the University of Wisconsin–Madison who was not engaged in the study, the new Leonardo-like rule is an improvement. However, she has reservations about the Russian group’s motivations. She claims that the live component of most trees goes considerably deeper than the thin surface layer.
McCulloh explains, “It’s truly species-dependent, and even age-dependent.” “A centimeter of living wood could be found in a large, old oak tree… “However, there are tropical tree species with very deep sapwood and possibly living wood for the majority of their cross sections.”
Grigoriev and colleagues put their rule to the test by photographing trees of various types and analyzing the branches to see if the real-world patterns matched the predictions. “A direct measurement of the features of a tree without touching it,” Grigoriev explains, “which can be significant when working with a live thing.”The rule applies to all deciduous trees researched by the researchers, even if they haven’t studied evergreens yet. “In addition to oak, birch, and chestnut, we’ve applied our methods to maple, linden, and apple,” Grigoriev explains. “They follow the Leonardo-like rule and have the same general structure.”
While it is conceivable to prove the rule by manually measuring branches, this would necessitate going into trees and inspecting all of the limbs, which is a dangerous exercise for both trees and scientists. “Note that not a single tree was injured during these studies,” the researchers write.