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Physics > Physics and Society

arXiv:2402.13520 (physics)
[Submitted on 21 Feb 2024]

Title:Fractal scaling and the aesthetics of trees

Authors:Jingyi Gao, Mitchell Newberry
Download a PDF of the paper titled Fractal scaling and the aesthetics
of trees, by Jingyi Gao and Mitchell Newberry
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    Abstract:Trees in works of art have stirred emotions in viewers
    for millennia. Leonardo da Vinci described geometric proportions
    in trees to provide both guidelines for painting and insights
    into tree form and function. Da Vinci's Rule of trees further
    implies fractal branching with a particular scaling exponent $\
    alpha = 2$ governing both proportions between the diameters of
    adjoining boughs and the number of boughs of a given diameter.
    Contemporary biology increasingly supports an analogous rule with
    $\alpha = 3$ known as Murray's Law. Here we relate trees in art
    to a theory of proportion inspired by both da Vinci and modern
    tree physiology. We measure $\alpha$ in 16th century Islamic
    architecture, Edo period Japanese painting and 20th century
    European art, finding $\alpha$ in the range 1.5 to 2.5. We find
    that both conformity and deviations from ideal branching create
    stylistic effect and accommodate constraints on design and
    implementation. Finally, we analyze an abstract tree by Piet
    Mondrian which forgoes explicit branching but accurately captures
    the modern scaling exponent $\alpha = 3$, anticipating Murray's
    Law by 15 years. This perspective extends classical mathematical,
    biological and artistic ways to understand, recreate and
    appreciate the beauty of trees.

Subjects: Physics and Society (physics.soc-ph); Popular Physics
          (physics.pop-ph)
Cite as:  arXiv:2402.13520 [physics.soc-ph]
          (or arXiv:2402.13520v1 [physics.soc-ph] for this version)
          https://doi.org/10.48550/arXiv.2402.13520
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Mitchell Newberry [view email]
[v1] Wed, 21 Feb 2024 04:09:25 UTC (7,792 KB)
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