Physics explains how rose petals get their iconic shape

Would a rose by any other shape smell as sweet? Maybe. Yet the shape of a rose is part of its beauty — and why these flowers fascinate scientists.

As they grow, the petals on a rose take on a distinct shape. Each one molds itself into a curved cup with points called cusps. At a glance, these petals may not look much different from those of other flowers. But scientists have now discovered that mathematically, the shape of a rose petal is different from that of other blooms.

To know how a petal develops its shape, you need to understand its underlying math, says Eran Sharon. He’s a physicist at Hebrew University of Jerusalem in Israel. He was part of a team that worked on the new research.

The shape of a rose arises because the flower gets “frustrated” as it grows, Sharon and his coworkers reported May 1 in Science. This discovery may inspire engineers to design new self-shaping materials for robots and electronics.

Not like other flowers

Outside forces shape most solid structures. Think of a building. Engineers must use supports and add materials such as concrete during its construction.

Plants, in contrast, are self-shaping. But the way a plant naturally tends to grow is not always allowed by the laws of physics, says Michael Moshe. He’s a physicist on Sharon’s team at the Hebrew University of Jerusalem.

When some force gets in the way of a plant growing into its preferred shape, this is called an incompatibility. And it can stress a plant.

Many plants have what’s known as Gauss incompatibility. It’s named for the 19th-century mathematician who discovered it: Carl Friedrich Gauss. This incompatibility arises when different parts of a plant grow at different rates. It may be the edge of a leaf growing faster than its center. The petals of carnation flowers and certain seed pods reduce this stress by forming a wavy edge.

“Gauss incompatibility” causes the petals of some blooms — such as this carnation — to form wavy edges. VIDOK/E+/Getty Images

In the past, scientists assumed that a rose’s shape arose the same way. But the sharp points of rose petal’s cusps look quite different from the smooth ruffles of carnations. So Sharon, Moshe and their coworkers suspected some other geometry was at play.

“By cutting small segments out of [rose petals] and looking at them in their relaxed shape, you can conclude what [shape] it wants to be,” explains Sharon.

“When we did that … the Gauss requirements were fulfilled,” he says. That is, rose petals’ preferred growth pattern would not lead to the same types of stress seen in plants with Gauss incompatibility.

So, what causes a rose petal’s iconic shape?

Stop and study the roses

To solve this mystery, the team ran a few experiments. They examined real rose petals, plastic replicas and computer models of petals. A different type of incompatibility better explained the rose’s shape, they found. It’s called MCP (for Mainardi-Codazzi-Peterson) incompatibility.

Unlike the Gauss type, this type depends mainly on a shape’s curvature. A rose petal does not maintain a smooth curve across its surface. As a result, a petal growing on a rose cannot maintain a smooth shape without tearing or folding. This MCP incompatibility leads to very specific points of stress.

On rose petals, that stress is expressed by forming sharp folds in the form of cusps.

To understand the shape of a rose petal, researchers studied 100 examples — both real (left) and fake (right).Dr. Yafei Zhang

To confirm this, the researchers designed replica petals with that incompatibility baked into them. These took on the exact shape of a real rose petals. “This proved [MCP] is completely sufficient to explain the shape,” Sharon says.

This is a “beautiful example” of how physics and geometry can offer insight into living tissues, says Suraj Shankar. He did not take part in the study. He does, however, study physics at the University of Michigan in Ann Arbor.

The new work also may have uses beyond understanding living things, he adds. Roses’ self-shaping traits could inspire materials for soft robots and flexible electronics.

“It is hard to predict what specific applications will emerge,” says Benny Davidovitch. He’s a physicist at University of Massachusetts Amherst. “It is very likely that beyond the aesthetic value of this work,” he says, “there will be real-world applications.”

At the end of the day, this work also shows just how interesting geometry can be, says Moshe — and how it can show up in the most unexpected places. “I think geometry is attractive because the questions are intuitive,” Moshe says. “But many times, the consequences are surprising and beautiful.”