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Related Experiment Video

Updated: Jun 18, 2026

LeafJ: An ImageJ Plugin for Semi-automated Leaf Shape Measurement

LeafJ: An ImageJ Plugin for Semi-automated Leaf Shape Measurement

Published on: January 21, 2013

The shape of a long leaf.

Haiyi Liang¹, L Mahadevan

¹School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.

Proceedings of the National Academy of Sciences of the United States of America

|December 8, 2009

Summary

This summary is machine-generated.

Plant leaf and algal blade shapes arise from elastic relaxation. Differential growth or stretching causes bending, leading to saddle shapes and rippled edges in these elongated structures.

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Area of Science:

Plant morphology
Biophysics
Materials science

Background:

Elongated plant leaves and algal blades exhibit characteristic saddle-like midsurfaces and rippled edges.
The underlying mechanisms generating these complex morphologies are not fully understood.

Purpose of the Study:

To investigate the physical principles governing the formation of leaf and algal blade shapes.
To develop a theoretical framework explaining the emergence of saddle shapes and ripples.

Main Methods:

Differential stretching of foam ribbons to mimic elastic relaxation.
Mathematical modeling of elastic sheets with lateral growth gradients.
Scaling concepts, stability analysis, and numerical simulations were employed.

Main Results:

Leaf and algal blade morphologies result from elastic relaxation via bending, following differential growth or stretching.
Increased relative growth strain leads to deformation from flat laminae to saddle shapes and/or undulations.
Localized growth strain at the edge can cause strongly localized ripples.

Conclusions:

The study provides a unified theory for the formation of elongated leaf and algal blade morphologies.
Geometric and growth control parameters dictate the shape space of laminae.
This framework enables comparative studies of leaf morphology across different species.