Leaf growth is conformal

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.