  Shape is one of the important characteristics for the structures observed in
living organisms. Whereas biologists have proposed models where the shape is
controlled on a molecular level [1], physicists, following Turing [2] and
d'Arcy Thomson [3], have developed theories where patterns arise spontaneously
[4]. Here, we propose a volume constraint that restricts the possible shapes of
leaves. Focusing on palmate leaves, the central observation is that developing
leaves first grow folded inside a bud, limited by the previous and subsequent
leaves. We show that growing folded in this small volume controls globally the
leaf development. This induces a direct relationship between the way it was
folded and the final unfolded shape of the leaf. These dependencies can be
approximated as simple geometrical relationships that we confirm on both folded
embryonic and unfolded mature leaves. We find that independently of their
position in the phylogenetic tree, these relationships work for folded species,
but do not work for non-folded species. This steric constraint is a simple way
to impose a global regulation for the leaf growth. Such steric regulation
should be more general and considered as a new simple means of global
regulation.
