ABQ Times

Albuquerque is a city familiar with fractals, hosting the Fractal Foundation and displaying fractal-themed billboards. These intricate patterns are formed by repeating simple processes at varying scales. The University of New Mexico's new study investigates how these patterns help humans perceive objects like trees.

The research, led by UNM Biology Professor Mitchell Newberry, focuses on branch diameter scaling and its role in tree perception. The study titled “Scaling in Branch Thickness and the Fractal Aesthetics of Trees” was published in the PNAS Nexus Journal.

Newberry's work extends beyond biology to art, analyzing tree depictions using mathematical equations for scaling. “We measure branch diameter scaling in trees and it plays the same role as fractal dimension, because it shows how many more tiny branches there are as you zoom in,” explained Newberry.

The team analyzed global artworks, including pieces from India, Japan, and Europe. Among them were L’Arbre de Vie by Gustav Klimt and Cherry Blossoms by Matsumura Goshun. They also examined two paintings by Piet Mondrian: De grijze boom (Gray Tree) and Bloeiende appelboom (Blooming Apple Tree).

In their analysis of the Sidi Saiyyed Mosque artwork, researchers found tree branches following Leonardo Da Vinci’s rule of branch diameter scaling with an exponent close to real trees. “We took a mathematical theory that was designed for biology and used it to look at artwork over centuries,” said Newberry.

Piet Mondrian’s Gray Tree adheres to branch diameter scaling with an exponent of 2.8, even though it uses only curved black strokes on a plain background. “If you show this painting to anyone, it's obviously a tree... So how does Mondrian convey a tree using just a few lines?” asked Newberry.

Conversely, Mondrian’s subsequent painting Blossoming Apple Tree does not follow this scaling rule. "If you look at that painting, people see dancers, fish scales... But the only difference between these two paintings—they’re both black strokes on a basically gray background—is the branch diameter scaling," explained Newberry.

Newberry asserts that without realistic branch diameter scaling, our perception of trees diminishes. He states that "Mondrian’s paintings show us that this branch diameter scaling description of trees is just so fundamental to how we perceive trees."

This research merges artistic insight with biological and mathematical perspectives to understand tree perception better. “Theorists, tree physiologists, artists and mathematicians all end up seeing the same thing in different ways,” stated Newberry.

While acknowledging artists' intuitive grasp of proportions, Newberry emphasizes the importance of mathematical benchmarks: “You could easily see the difference between scaling exponents... if you have a discerning eye.”