Scientists Finally Solve The Mystery Behind Rose Petals’ Unique Shape

Research led by Yafei Zhang, Hebrew University of Jerusalem

In a nutshell

• Rose petals get their pointed shapes from a unique geometric conflict—not uneven growth rates.
• The shape emerges due to “Mainardi-Codazzi-Peterson incompatibility,” a built-in mechanical mismatch.
• This discovery could inspire shape-shifting materials in engineering and design.

Ever notice how rose petals curl at the edges with those elegant pointed tips? For centuries, artists have celebrated these distinctive shapes in paintings and poetry, but the science behind them remained elusive—until now.

New research published in Science has unlocked the mystery, revealing that roses shape themselves through a mathematical mismatch that happens during growth. Unlike other flowers that get their shapes from varying growth rates, roses form their characteristic points because of a phenomenon called “Mainardi-Codazzi-Peterson incompatibility”—basically, a built-in geometric conflict.

The research team from the Hebrew University of Jerusalem studied Red Baccara roses and about 100 petals from various rose species. They noticed a clear pattern: young petals near a flower’s center have smooth edges, while older petals develop polygon-like shapes with distinct points.

To figure out why this happens, they cut narrow strips from different areas of the petals. Strips cut along the edge stayed flat, but strips cut from center to edge curved downward—revealing different growth patterns in different directions.

This led to a breakthrough discovery: rose petals grow with curvature only in the radial direction (from center to edge), not around the circular edge. As growth continues, this mismatch creates what engineers call “geometric frustration”—the material physically cannot exist in its preferred state without distorting.

“Their distinctive shape emerges from a different type of geometric incompatibility,” the researchers write in the paper, referring to this specific mathematical conflict.

Testing their theory, the scientists created simplified models of disc-shaped petals through computer simulations and physical experiments using a biodegradable plastic. By programming these models with the same growth patterns seen in real roses, they reproduced the transformation from smooth edges to pointed tips.

The team confirmed their findings with a clever experiment: they gently moved a newly formed point on a young petal to a different spot along the edge, then let the flower keep growing. The original location grew normally with a rounded edge, while the new location developed a concave edge—proving that the point itself changes how tissue grows.

This discovery goes beyond explaining pretty flowers. It reveals a mechanism that could transform manufacturing and engineering, where the same principles might help create materials that automatically form specific shapes without external manipulation.

Traditional methods for creating complex curves in thin materials require outside forces, but this study shows how well-designed growth patterns can spontaneously create sophisticated shapes. From architecture to medical devices, the principles behind rose petal formation might someday help engineers create structures that automatically fold into useful forms.

The research illuminates how a simple growth pattern creates a feedback loop between shape and biology: the symmetrical growth causes geometric incompatibility, creating points and concentrating stress, which then redirects subsequent growth—nature’s elegant solution to a mathematical problem.

Funding and Disclosures

The research was funded by the Israel Academy of Sciences and Humanities and Council for Higher Education Excellence Fellowship Program for International Postdoctoral Researchers, the United States-Israel Binational Science Foundation (grant 2020739), and the Israel Science Foundation (grants 2437/20 and 1441/19). The authors declared no competing interests.

Publication Information

The paper titled “Geometrically frustrated rose petals” was authored by Yafei Zhang, Omri Y. Cohen, Michael Moshe, and Eran Sharon from the Racah Institute of Physics at the Hebrew University of Jerusalem, Israel. It was published in Science on May 1, 2025, and accepted on February 25, 2025, after being submitted on September 10, 2024.