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💧🌏 Greg Cocks

Scaling In Branch Thickness And The Fractal Aesthetic Of Trees [In Art From Da Vinci To Mondrian]
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academic.oup.com/pnasnexus/art <-- shared paper
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[not my usual fare, but love the spatial mathematical components, although the maths is way over my head!]
#spatial #maths #mathematics #art #painting #representation #daVinci #LeonardodaVinci #MurraysLaw #tree #vegetation #fractal #fractals #α #biology #artwork #radiusscalingexponent #branches #branching #nature #naturalpatterns #proportions #physiology #Mondrian #aesthetic #aesthetics #scale #scaling

a) da Vinci’s sketch of a tree illustrates the principle that combined thickness is preserved at different stages of ramification. b) Transects A and B have the same combined thickness and so limbs a and b together must have the same thickness as c. This has been taken to imply that c) combined cross-sectional area (⁠πR²⁠) is preserved across branching. Likewise, d) such transects can count the number of branches n that have radius approximately r to derive a fractal scaling relationship. Source: (a) from Institut de France Manuscript M, p. 78v.
sketch from one of Leonardo da Vinci's notebooks illustrating his original rules of trees
The scaling exponent α (a) determines the amount of detail at a given resolution and (b) proportions among adjoining boughs.
Trees in artwork across centuries, cultures, and styles exhibit fractal scaling. a) carved stone window screen of Sidi Saiyyed Mosque, Ahmedabad, Gujarat, India (1573 CE). b) Cherry Blossoms, Matsumura Goshun (1752–1811), ink on paper. c) L’Arbre de Vie (Tree of life), Gustav Klimt (1909), oil on canvas. d) data and inference of α±95% CI in two replicate measurements for each work along with simulated and living trees. Dotted vertical lines indicate the cutoff for excluding small-scale effects. Diameters from simulated and living trees are divided by this minimum value and therefore the horizontal axis is unitless.
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