A study by academicians at the University of Michigan and the University of New Mexico has uncovered that our perception of trees within artistic works is guided by a mathematical rule called the branch diameter scaling exponent. This finding reinforces Leonardo da Vinci’s historic insights into the configurations of tree branches.
The investigative team includes Jingyi Gao, who completed her undergraduate studies at U-M’s Mathematics Department and is currently pursuing her Ph.D. at the University of Wisconsin, and Mitchell Newberry, a research assistant professor at UNM. They delved into how the ratio of tree branch sizes affects our recognition of a tree’s form. Newberry expressed how their work could be applied universally, remarking, “What we have identified is a principle that appears to be pervasive across both the artistic and natural worlds.”
Fractal Patterns as a Lens for Artistic Interpretation
Fractals, patterns that recur at varying scales, are found in both natural phenomena like frost patterns and biological systems including vascular networks and arboreal structures. These branching patterns, akin to fractal dimensions, reveal how smaller branches originate from larger ones.
Gao highlights the uncomplicated nature of the mathematical underpinnings of the study, which are grounded in the Pythagorean theorem. She explains, “Fractals are simply shapes that replicate themselves… Observing a tree, you see how its branches bifurcate. The resulting smaller branches mirror the image of the larger, parent branch.”
The team’s research spanned artworks from various cultures and eras, ranging from 16th-century Indian sculptures to abstract pieces by the 20th-century Dutch artist Piet Mondrian. Newberry found Mondrian’s creations especially illuminating – some compositions maintained their arboreal character through specific branch scaling whereas others, which deviated from this scaling, morphed into abstract conceptions no longer reminiscent of trees.
Published in PNAS Nexus, this interdisciplinary study emphasizes the fusion of art and mathematics, introducing the idea that scientific rules can inform our appreciation of beauty, extending beyond subjective interpretations. Gao and Newberry praise the collaborative efforts of the Center for the Study of Complex Systems at U-M for integrating mathematics and aesthetics.
As this research eloquently connects quantifiable mathematical laws with the personal experience of art, it not only corroborates da Vinci’s early observations but also enhances our comprehension of artistic expression across various genres and traditions..
