The researchers also dissected the leaves of the plantain lily to show that elastic strain resulting from differential growth led to the patterns seen in real leaves. From this simple experiment, the researchers then developed a mathematical model explaining the shape, using a combination of scaling concepts, stability analysis, and numerical simulations.

"While the phenomena has been studied previously, researchers did not consider the role of finite size of a leaf on the stability or the effect of boundaries. Further, our study characterizes, mathematically, the range of parameters that quantify the shape and diversity in leaf morphology," adds Mahadevan.

The resulting model has application in understanding a variety of artificial systems such as non-uniform thermal expansion, hydraulic（水力的，水压的） swelling（膨胀的）, and plasticity induced shape changes in thin laminae.

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