Photo by
Benny Dudkevitch/TPS-IL on 8 May, 2025
The Secret Geometry of Roses May Shape the Future of Robotics, Scientists Say
Jerusalem, 8 May, 2025 (TPS-IL) -- The soft, curving edges of rose petals have long captivated poets, artists, and scientists alike. Now, Israeli scientists have uncovered the hidden geometry that gives these petals their signature shape, revealing not just a botanical secret but a new blueprint for future engineering that could lead to more flexible electronics and architectural elements that “grow.”
A Hebrew University study recently published in the peer-reviewed Science found that the iconic cusp-like edges of rose petals were shaped by different mechanisms than previously thought.
For years, scientists assumed that structures like leaves and petals developed their forms mainly through Gauss incompatibility — a type of geometric mismatch that causes surfaces to bend and twist during growth.
However, when the researchers — led by Prof. Moshe Michael and Prof. Eran Sharon at the Racah Institute of Physics — closely examined rose petals, they found no signs of Gauss incompatibility at work. Instead, they discovered that the petals’ shapes are governed by a geometric principle called Mainardi-Codazzi-Peterson incompatibility.
Gauss incompatibility causes smooth warping, which is expressed by bending, wrinkling, twisting petals. MCP incompatibility, however, results in sharper features such as cusps, folds and sharp undulations. In the case of rose petals, as they grow, stress concentrates at the edges. Because of MCP incompatibility, the petal naturally forms dramatic, pointed curves — not random wrinkles but a predictable pattern governed by geometric necessity.
“This research brings together mathematics, physics, and biology in a beautiful and unexpected way,” said Sharon. “It shows that even the most delicate features of a flower are the result of deep geometric principles.”
The team combined computer modeling, laboratory experiments, and mathematical simulations to test their theory, and consistently found that MCP stress — and not Gauss stress — was responsible for the unique curves of rose petals. As the petal grows, stress builds up particularly at the edges, causing the petal to form its signature curls and cusps.
One of the most intriguing findings is the feedback loop between growth and stress, the scientists said. As stress concentrates at the cusps, it directs how and where the petal continues to grow. In this way, geometry and biology are locked in a continuous dialogue, with form and function shaping each other.
“It’s astonishing that something as familiar as a rose petal hides such sophisticated geometry,” said Michael. “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.”
The findings open intriguiging possibilities for soft robotics, flexible electronics, and smart or self-morphing materials.
Materials that can change shape precisely without needing motors, joints, or external controls could lead to softer, more flexible robots, particularly 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 morphable electronic circuits and displays that adjust their form depending on their function. Moreover, the discovery of MCP incompatibility gives engineers a new tool to design materials that “program” themselves to curl, fold, or bend into intricate shapes without manual assembly. This could revolutionize packaging, construction materials, and deployable structures such as satellites unfolding in space.
The study also opens a door for architectural elements that “grow” into position or change shape based on environmental conditions like heat, humidity, or light.
The research may also have medical applications. Since biological tissues also experience internal stresses during growth, these findings could eventually help in designing scaffolds for growing organs or tissues that need to take on complex shapes naturally.
