How Do Trees Grow?
Leonardo da Vinci, the master of Renaissance art and science, had crafted his “rule of trees” over 500 years ago which actually states that if you fold all of a tree’s branches upward, they will unite to form a continuous trunk with the same surface area. Modern publications have proven the validity of da Vinci’s rule, even though da Vinci did not collect experimental data (that is known) to formulate this hypothesis. Da Vinci’s opinions on tree branch directionality and size relative to their parent branch are elucidated in Figure 1.
For his time, Leonardo da Vinci’s interest in tree anatomy was unusual. During the 1400s and early 1500s, trees and other scenery were rarely depicted in art and other areas of life. The drawings and annotations in this image add to da Vinci’s overall interest in using scientific qualities and relationships in paintings to make them appear more multidimensional and realistic.
However, researchers state, from an article released April 13 in Physical Review E, that da Vinci’s rule hadn’t had included all types of trees, though it was a brilliant head starter, for nowadays experimenters and developed 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 describes the thickness of the branches, while the length of the branch was not taken into account”, and noted, “Therefore, the description using the older rule is not complete.”
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 criterion integrates limb widths and lengths and predicts that long branches will be thinner than short ones, using the 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 the surface area of branches and overall tree structure demonstrates that tree construction is guided by the living, outer layers. “As if the tree were a two-dimensional entity,” the authors write in their study, “the life of a tree flows according to the laws of conservation of the area in two-dimensional space.” In other words, it’s as if any tree’s structure is determined solely by two dimensions: the width of each limb and the distance between branchings on a limb. As a result, the new rule works particularly effectively when trees are depicted in two dimensions in a painting or on a screen.
Works Cited
https://editions.covecollective.org/content/da-vincis-rule-trees
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3979699/
https://www.insidescience.org/news/uncovering-da-vincis-rule-trees
https://www.sciencenews.org/article/leonardo-da-vinci-rule-tree-branch-wrong-limb-area-thickness
