A growing leaf is a prototypical active solid, as its active units, the cells, locally deform during the out-of-equilibrium process of growth. During this local growth, leaves increase their area by orders of magnitude, yet maintain a proper shape, usually flat. How this is achieved in the lack of a central control, is unknown. Here we measure the in-plane growth tensor of Tobacco leaves and study the statistics of growth-rate, isotropy and directionality. We show that growth strongly fluctuates in time and position, and include multiple shrinkage events. We identify the characteristic scales of the fluctuations. We show that the area-growth distribution is broad and non-Gaussian, and use multiscale statistical methods to show how growth homogenizes at larger/longer scales. In contrast, we show that growth isotropy does not homogenize in time. Mechanical analysis shows that with such growth statistics, a leaf can stay flat only if the fluctuations are regulated/correlated.

生长中的叶子是典型的活性固体，因为它的活性单元，即细胞，在生长失衡过程中局部变形。在这种局部生长过程中，叶子的面积增加了几个数量级，但仍保持适当的形状，通常是平坦的。这是如何在缺乏中央控制的情况下实现的，尚不得而知。在这里，我们测量烟草叶的面内生长张量并研究生长速率、各向同性和方向性的统计数据。我们表明增长在时间和位置上波动很大，并且包括多个收缩事件。我们确定了波动的特征尺度。我们展示了面积增长分布是广泛的和非高斯分布，并使用多尺度统计方法来展示增长如何在更大/更长的尺度上均匀化。相比之下，我们表明生长各向同性不会及时均匀化。