Scientists discover math behind tree patterns in famous artworks

In a groundbreaking study published in the journal PNAS Nexus, researchers have revealed how the artistic representations of trees by renowned painters, including Leonardo da Vinci and Piet Mondrian, reflect the mathematical principles governing tree branch patterns in nature. The study highlights that trees commonly exhibit a self-similar branching pattern characterized by fractals, where the same structural formations recur at diminishing scales from thick trunks to thin branch tips. This mathematical analysis explored the scaling relationship of branch thickness in various artworks, showing that renowned artists conveyed these natural patterns in their creations. The researchers investigated multiple cultural artworks, including a 16th-century mosque in Ahmedabad, India, Japanese Edo period paintings, and Mondrian’s abstract works. They derived mathematical rules outlining the proportions and approximate number of branches with differing diameters, verifying that the parameter alpha, which illustrates the relationship between branch thicknesses, in various artworks falls within a range of 1.5 to 2.8. This range corresponds closely to that observed in actual trees, affirming that artists across civilizations have unconsciously incorporated these natural patterns into their representations of trees. Leonardo da Vinci, recognized for his keen observations of nature, noted that as tree limbs branch out, they maintain their thickness. He proposed that when the thickness of a branch equals the combined thicknesses of its two smaller branches, the parameter alpha would be calculated as two. The findings from this study suggest that even abstract representations of trees can be appreciated as such if a realistic parameter alpha is applied. The researchers assert that the mathematical relationships uncovered can aid in recognizing abstract depictions as trees when the typical fractal dimensions are corresponded appropriately. Ultimately, this study offers a novel perspective to appreciate and replicate the beauty of trees within art, showcasing the interplay between scientific analysis and artistic representation. By bridging the study of nature with human creativity, this research not only uncovers the hidden mathematical principles in artwork but also emphasizes the significant relationship between art and science, reinforcing how each can enhance our understanding of the other, especially in representation of the natural world.