Leaf growth is conformal

TL;DR

This paper demonstrates that leaf growth patterns can be modeled as conformal transformations, allowing accurate prediction of local displacement fields from simple contour observations, revealing a universal approach for isotropic tissue growth analysis.

Contribution

The study introduces a conformal mapping method to analyze and predict leaf growth dynamics, providing a new quantitative tool for morphogenesis research.

Findings

Predicted displacement field matches experimental data with 92% accuracy.

Conformal transformations effectively model isotropic growth in plant leaves.

Method applicable to any 2D tissue with isotropic growth patterns.

Abstract

Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a later stage. Based on the mapping we predict the local displacement field in the leaf blade and find it to agree with the experimentally measured displacement field to 92%. This approach is applicable to any two-dimensional system with locally isotropic growth, enabling the deduction of the whole growth field just from observation of the tissue contour.