How plants make flat leaves: conformal maps and developmental mechanisms that might generate them

1 June 2018

Graeme Mitchison
Sainsbury Laboratory and Centre for Mathematical Sciences
University of Cambridge


Most of the leaves we see around us are approximately flat. There are obvious advantages for light collection in having flat leaves. What developmental mechanisms ensure that leaves are flat? Data from Arabidopsis leaves [1] show that growth is fairly isotropic, i.e small regions expand equally in all directions. Mathematically speaking, we can think of flat leaves as planar regions, and maps of the plane that are isotropic are called conformal maps. There is a well developed theory of conformal maps, which provides a useful tool for interpreting the data on leaf growth [2], and allows one to make inferences about underlying developmental mechanisms.


  1. L Remmler, A-G Rolland-Lagan, "Computational method for quantifying growth patterns at the adaxial leaf surface in three dimensions", Plant Physiol 159:27-39 2012. PDF.
  2. G Mitchison, "Conformal growth of Arabidopsis leaves", J Theor Biol 408:155-66 2016. bioRxiv.

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