The Hidden Rules Behind Leonardo da Vinci’s Trees

Image: Leonardo da Vinci, Public domain, via Wikimedia Commons

In previous articles, we have spent considerable time discussing Leonardo da Vinci’s patronage under Duke Ludovico Sforza. Much of that discussion has focused on the planned bronze horse monument intended to honor the Duke’s father. However, this was only one of many projects Leonardo undertook while living in Milan. During this same period, for example, he received the commission for The Last Supper.

Leonardo constantly looked for connections between nature and human life. During this same period, while conducting his fossil studies, he also began making meticulous observations and sketches of trees. The hypotheses he developed in the late fifteenth century have held up under modern scrutiny (Moore, 2024). His three major observations can be summarized as follows: trees grow proportionally, nature reuses successful designs, and nature continually builds through self-similarity. Leonardo believed that nature followed consistent rules of branching, repeated across everything from trees to veins to entire landscapes (Moore, 2024).

Leonardo’s first major observation centered on the proportional relationship between tree branches and the thickness of the trunk. He argued that although branches divide and become smaller, their combined thickness remains equal to that of the trunk. According to Kathryn Moore (2024), Leonardo’s notes represent the first recorded observation of this rule of proportion. She also notes that modern science has found his observations to be largely accurate, with only minor revisions.

The second major finding is that nature, once it discovers a design that works, reuses that design across the natural world. Leonardo’s strongest evidence for this idea was the similarity between the branching structure of trees and the human circulatory system. His study of the body went beyond external observation; throughout his life, he dissected cadavers to better understand internal anatomy.

Moore (2024) describes one such dissection in which Leonardo focused on the liver of an elderly man, recording his observations through a series of detailed sketches. These drawings are accompanied by very little text, as Leonardo believed that words alone were insufficient to explain what he observed.

From these studies, Leonardo concluded that the circulatory system functioned much like a tree: large, thick vessels connect to the heart and gradually divide into smaller, more delicate branches as they extend throughout the body. He also hypothesized that the heart—not the liver—served as the center of the circulatory system, challenging earlier medical traditions (Moore, 2024).

Leonardo’s third major observation was that nature continually builds through self-similarity. As a tree grows, its branches do not simply spread outward in random directions; instead, each branch forms a smaller version of the whole, repeating the same basic pattern at every level. This creates a structure in which large branches divide into smaller ones, which then divide again, maintaining the same overall form even as the scale changes. Moore (2024) notes that this process results in what appears to be a series of ever-smaller versions of the original tree, demonstrating that growth in nature is not chaotic but governed by consistent and repeating patterns.

In the next article, we will examine another pattern that fascinated Leonardo as we turn to the art of da Vinci knots.

Further Reading

Moore, K. (2024). Leonardo da Vinci and the arboreal architecture of life. CrossCurrents, 74(3), 304–

324. https://www.jstor.org/stable/10.2307/27372631