  Lotus leaves floating on water usually experience short-wavelength edge
wrinkling that decays toward the center, while the leaves growing above water
normally morph into a global bending cone shape with long rippled waves near
the edge. Observations suggest that the underlying water (liquid substrate)
significantly affects the morphogenesis of leaves. To understand the
biophysical mechanism under such phenomena, we develop mathematical models that
can effectively account for inhomogeneous differential growth of floating and
free-standing leaves, to quantitatively predict formation and evolution of
their morphology. We find, both theoretically and experimentally, that the
short-wavelength buckled configuration is energetically favorable for growing
membranes lying on liquid, while the global buckling shape is more preferable
for suspended ones. Other influencing factors such as stem/vein, heterogeneity
and dimension are also investigated. Our results provide a fundamental insight
into a variety of plant morphogenesis affected by water foundation and suggest
that such surface instabilities can be harnessed for morphology control of
biomimetic deployable structures using substrate or edge actuation.
