ArticleScientific reports2018
The mechanical principles behind the golden ratio distribution of veins in plant leaves.
Article in Scientific reports, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Engineering principles in plant metabolism: integrating control, mechanics, and transport under dynamic environments.Plant physiology · 2026Review
- Mechanical and Energy Absorption Properties of Porous Royal Water Lily Leaf Vein Cross-Sections Under Quasi-Static Axial Loading.Biomimetics (Basel, Switzerland) · 2026Article
- Generative adversarial networks enable biomimetic topology fusion with balanced mechanical performance and aesthetic quality.Scientific reports · 2026Article
- Three levels of heterogeneity - growth of Arabidopsis leaf epidermis.BMC plant biology · 2025Article
- Analyzing Mushroom Structural Patterns of a Highly Compressible and Expandable Hemostatic Foam for Gastric Perforation Repair.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2024Article
- Exploring the role of loop tunnels in enhancing termite food transport efficiency: A simulation approach.Heliyon · 2024Article
- Effects of the surface irregularity of termite tunnels on food transport efficiency: a simulation study.Journal of insect science (Online) · 2023Article
- The golden number seen in a mechanical oscillator.Scientific reports · 2022Article
- Multi-functional topology optimization ofJournal of the Royal Society, Interface · 2022Article
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Authors and funding
11 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Tree leaves are commonly composed of thin mesophyll, carrying out photosynthesis under sunlight, and thick veins. Although the role of leaf veins in water transportation has been known for a long time, their role in providing structural support and guaranteeing large sunlighted area was rarely studied and remains elusive. Here, with use of a novel inverse optimization approach, we aim for uncovering the material design principle behind the unique pattern of venation. It is intriguing to observe that an almost Golden Ratio (GR) distribution of leaf veins always provides optimized structural behavior. Specifically, our research reveals, for the first time, that this unique GR distribution of relatively strong vein material is helpful for maximizing the bending stiffness and leading to a large sunlighted area which is vital for the photosynthesis process of a leaf. Moreover, the GR distribution of leaf veins is also observed in a wide class of plant leaf geometries (i.e., shape, thickness), where experimental evidence is provided for the optimized results. Therefore, our findings can not only serve to explain the mystery of veins GR distribution but also provide widely applicable guidelines on designing soft structures with exceptional mechanical performances.
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