  What are the general principles that allow proper growth of a tissue or an
organ? A growing leaf is an example of such a system: it increases its area by
orders of magnitude, maintaining a proper (usually flat) shape. How can this be
achieved without a central control unit? One would think that a combination of
uniform growth with viscoelastic rheology would allow that. Here we show that
that the exact opposite process is in action: the natural growth of the leaf
surface strongly fluctuates in time and position. By combining high resolution
measurements and multi-scale statistical analysis, we suggest a paradigm-change
in the way leaf growth is viewed. We measure the in-plane tissue growth of
Tobacco leaves in Lagrangian coordinates in 3D and study the statistics of
three scalar fields associated with the tensorial growth field: The growth
rate, its isotropy and directionality. We identify the governing time and
length scales of the fluctuations in the growth rate, and capture abundant
switching between local area swelling and shrinking, when measured in high
resolution. At lower spatio-temporal resolution the growth rate field becomes
smooth. In contrast, the anisotropy field increases over time. Finally, we find
significant differences between growth measured during day and night. The
growth at night is found to be more intermittent, with shorter correlation
lengths and no global directionality. Despite its fluctuative nature, growth
fields are not random, thus carry information about growth regulation. Indeed,
mechanical analysis shows that a growing leaf can stay flat only if the
measured fluctuations are regulated/correlated. Our measurements suggest that
the entire statistics of growth fields, and not just their means, should be
studied. In particular, the regulation of such fields and the link between
their characteristics and the global geometry of a leaf should be studied.
