Researchers uncover unique rose petal geometry, paving way for new smart materials

JERUSALEM, May 5 (Xinhua) -- A team of physicists at the Hebrew University of Jerusalem has uncovered the hidden geometric principles behind the unique shape of rose petals, which may lead to innovations in flexible electronics, soft robotics, and bio-inspired design.

For the past two decades, scientists believed that the shapes of structures like petals and leaves formed due to "Gauss incompatibility," a geometric mismatch that causes wavy patterns, less defined edges, and a lack of sharp cusps. However, roses, unique among flowers, are Gauss-compatible. The highly localized, singular cusps emerging from the edges of their petals cannot be explained by currently known geometric mechanisms.

In the study featured on the cover of the latest issue of Science, researchers built computer models to simulate how the roses might grow and bloom. They then created bendable plastic disks to simulate petals and the possible ways they could grow under the constraints of real roses.

They describe the mathematics that shapes growing rose petals: growth creates a geometric conflict, forcing petals into forms where the relaxed state cannot be smoothly realized in three-dimensional space without distortion. This frustration shapes the rose's beauty, focusing stress into sharp, elegant edges.

According to the researchers, the petals' shape is strongly impacted by the frustration known as the Mainardi-Codazzi-Peterson incompatibility, in which geometric compatibility conditions inherent in a surface made of a particular material are violated, leading to forces that generate rolling and sharp edges.

These findings could lead to advances in materials that, like petals, change shape as they grow or are activated.

One key discovery is the feedback loop between growth and stress, with stress at the cusps influencing how the petals grow, demonstrating the interplay between biology and geometry.

According to the researchers, even a flower's most delicate features follow deep geometric principles, offering a powerful new tool for engineers and scientists to mimic nature in manmade systems.

They concluded that this discovery reshapes the understanding of how complex forms emerge and opens new possibilities for designing elegant, self-shaping materials. ■