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Leaf growth is conformal

Abstract : Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. Wecompute 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.
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Karen Alim, Shahaf Armon, Boris I. Shraiman, Arezki Boudaoud. Leaf growth is conformal. Physical Biology, Institute of Physics: Hybrid Open Access, 2016, 13 (5), pp.1-6. ⟨10.1088/1478-3975/13/5/05LT01⟩. ⟨hal-02633578⟩

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