The secret geometry of roses could shape the future of robotics, according to Israeli scientists

The soft, curved edges of rose petals have long fascinated poets, artists, and scientists.

Now, Israeli scientists have uncovered the hidden geometry that gives these petals their distinctive shape, revealing not only a botanical secret but also a new blueprint for future engineering that could lead to more flexible and "growing" electronics and architectural elements.

A Hebrew University study, recently published in the journal Science, has revealed that the iconic pointed edges of rose petals were formed by different mechanisms than previously thought.

For years, scientists have hypothesized that structures like leaves and petals develop their shapes primarily through Gaussian inconsistency, a type of geometric inconsistency that causes surfaces to bend and distort as they grow.

However, when the researchers, led by Prof. Moshe Michael and Prof. Eran Sharon of the Racah Institute of Physics, carefully examined the rose petals, they found no signs of incompatibility.

Instead, they discovered that petal shapes are governed by a geometric principle called the “Mainardi-Codazzi-Peterson incompatibility” (MCP).

“Gaussian inconsistency” causes uniform deformation, which manifests as bending, wrinkling, and twisting of the petals.

MCP incompatibility, on the other hand, results in sharper features such as pronounced cusps, folds, and undulations.

In the case of rose petals, during growth, stress is concentrated at the edges. Because of the MCP incompatibility, the petal naturally forms sharp, pronounced curves—not random folds, but a predictable pattern governed by geometric necessity.

"One of the most interesting findings is the curvature of the response between growth and stress," the scientists said.

As stress is concentrated at the tips of the petal, it directs how and where the petal continues to grow. In this way, geometry and biology are locked in a constant dialogue, with form and function shaping each other.

“It's surprising that something as familiar as a rose petal hides such sophisticated geometry,” Michael said.

"What we discovered goes far beyond flowers - it's a window into how nature uses shape and stress to guide growth in everything from plants to synthetic materials," he added.

The findings open up exciting possibilities for soft robotics, flexible electronics, and smart or self-changing materials.

Materials that can change shape precisely without the need for motors, joints, or external controls could lead to softer and more flexible robots, especially surgical robots and search-and-rescue robots.

Understanding how to control shape through internal stress like petals do could help engineers create flexible, foldable, or changeable electronic circuits and displays that adjust their shape depending on their function.

Furthermore, the discovery of MCP incompatibility gives engineers a new tool to design materials that “program” themselves to bend, fold, or flex into complex shapes without manual assembly. This could revolutionize packaging, building materials, and deployable structures such as satellites deployed in space.

The study also opens a door for architectural elements that "grow" into position or change shape based on environmental conditions such as heat, humidity or light.

The research could also have medical applications. Since biological tissues also experience internal stresses during growth, these findings could ultimately help design scaffolds for growing organs or tissues that need to naturally take on complex shapes.