💧🌏 Greg Cocks
Scaling In Branch Thickness And The Fractal Aesthetic Of Trees [In Art From Da Vinci To Mondrian]
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https://academic.oup.com/pnasnexus/article/4/2/pgaf003/7996468 <-- 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
Feb 13, 2025 at 8:23pmWeb
Show threadTillman ReuterFeb 13, 2025
@GregCocks in functional-structural plant modelling the a^2+b^2=c^2 is commonly used. An exponent of 2 promotes the hypothesis, that area is preserved through branching. This makes sense for plants that carry water through their whole stem (xylem) because the area then relates to water velocity and if it would shrink through branching water would have to accelerate at the branching point.
Show threadTillman ReuterFeb 13, 2025
@GregCocks a+b=c on the other hand makes sense from the phloem perspective. For all assimilates transported through the bark the amount of bark should stay constant throughout the branching point. And circumference relates linearly to radius instead of quadratically (like area does)