seeing double

Alien-like vegetables have mathematical “memory” — study

There’s more going on in a Romanesco than meets the eye.

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Romanesco broccoli vegetable represents a natural fractal pattern and is rich in vitimans. First doc...

It is technically a vegetable, but we’d like to make the case that Romanesco cauliflower is an otherworldly sight to behold.

The gentle, green conical towers sprouting from its surface — made themselves from even smaller conical towers — are mesmerizing. And the reason is more to do with math than flavor — the surface of Romanesco is a textbook example of a natural fractal.

These organic patterns appear throughout nature. But until now scientists have known little about how the self-similar patterns in sunflower heads, cauliflower, or the centers of daisies actually develop. The answer may be more human than you’d expect.

What’s new — In a study published Thursday in the journal Science, an international team of computational biologists uses 3D modeling to reveal what’s at the root of Romanesco’s breathtaking appearance. What they found runs contrary to the very idea of Romanesco as an organic, wild thing, rather than something artificial — the fractal patterns, known as curds by plant biologists, appear to be a “memory” of a past state, one that was influenced more by humans’ eating habits than by anything else.

First, the team built a virtual network of the plant’s main regulatory genes including those involved in curd and flower development. They then investigated how these curds could be triggered in a plant with cauliflower-like structures, Arabidopsis thaliana.

While this delicate, white petaled flower has little resemblance to Romanesco in its wild form, the team found that modifying its genes in a 3D model could trigger remarkably similar curd formation.

Romanesco is a variety of cauliflower, yet its beauty almost transforms it beyond a mere vegetable.


Why it matters — Part of the reason why this research is so illuminating is that it reveals a new facet of our relationship with the food we eat, explains Christophe Godin, a senior author on the paper and senior researcher at INRIA Paris Research Center in France.

“Self-similarity allows high curd compactness, which attracts humans for food,” Godin tells Inverse.

“Conspicuous fractal curds also attract humans by their fascinating beauty. We could say at least that cauliflowers and romanesco benefit from the symbiosis with humans that cultivate them and make them proliferate.”

Godin also says that this new work could lead to the “development of bio-inspired fractal mathematical constructions.”

“This provides new ways to think about fractals as growing structures with local distributed growth regulation,” Godin says.

Here’s the background — First documented in Italy in the 16th century, plant biologists have known for a while that Romanesco’s curds (as the truncated nubbins growing off its surface are called) are the result of flowering stems failing to reach maturity. However, how genes or mutations inside the plant dictate this process remained up for debate.

A nautilus shell is another example of a mathematical ratio — the Golden Ratio — appearing in nature.


Fractals in nature are a beautiful, albeit sometimes eery, reminder of the universe’s strange inner workings, and this research could offer an opportunity to pull back that curtain a little further.

The word fractal is derived from the Latin word fractus which means “broken” or “fractured” and is used to describe repeating patterns in nature, design, or human physiology. Branching trees, human lungs, and data management systems are some ways fractals show up in our daily life.

“Fractal curds also attract humans by their fascinating beauty.”

The Fibonacci Sequence is also another common way to describe a particular kind of fractal that grows larger and larger with new branches.

Francois Parcy, a senior author on the paper and plant physiology researcher at the Laboratoire Physiologie Cellulaire et Végétale in France, tells Inverse that a branching fireworks display is a good example. The Fibonacci Sequence is also what gives rise to the Golden Ratio — a curve that evokes both beauty and perfect order.

With the exponential growth of its curds, Romanesco falls into this mathematical ideal of beauty. Which Godin says isn’t necessarily beneficial for the plant — aside from how this pattern attracts human cultivators.

How they did it — By tweaking the genes introduced to their model plant, the team was able to demonstrate that the growth of flower buds could be drastically changed by introducing specific mutations — to be precise, mutations in the gene AP1/CAL.

This human-selected gene variation allowed the team to determine that a form of “memory” was responsible for the plant's recursive and immature curd growth — the fractals that draw us to eat a Romanesco and feel somehow different from if we ate a standard white, fluffy cauliflower.

Parcy explains the process a little more to Inverse:

“A stem normally grows with leaves and you rarely have many stems piling up on each other with elongation,” Parcy says “Memory of the floral state generates stems with no leaves — flowers have no leaves — and free from the control of apical dominance.” This refers to a process that restricts bud growth beneath a new shoot.

“We have understood how a few perturbations can change a flowering shoot into cauliflowers or in Romanesco,” adds Parcy. “And how they can be changed drastically by human selection.”

By introducing different genes to their model plant, the team demonstrated that it was possible to grow a new Romanesco-like surface.

Azpeitia et al. / Science

What’s next — As delicious as this new finding is, the team has not cracked the code on fractals in food, Parcy says. There are still plenty more plants that show these recurring, mathematical patterns out there to study, he says.

“We understand well the Arabidopsis cauliflower but we know there must be more mutations to explain the compact cauliflower curd,” he says.

“We have not found the nature of all the mutations that are responsible for the curd shape or the Romanesco increased bud production,” he adds.

But, as they do here, there is a new avenue opening up for future research, in which labs can use genetic technology to potentially transform plants as we know them, and create new patterns using these organic blueprints.

“A recent paper provides hundreds of sequences for cabbage broccoli and cauliflower that could be used within our framework to go one step further,” he says.

“Maybe we could create cauliflowers from other plants!”

Abstract: Throughout development, plant meristems regularly produce organs in defined spiral, opposite, or whorl patterns. Cauliflowers present an unusual organ arrangement with a multitude of spirals nested over a wide range of scales. How such a fractal, self-similar organization emerges from developmental mechanisms has remained elusive. Combining experimental analyses in an Arabidopsis thaliana cauliflower-like mutant with modeling, we found that curd self-similarity arises because the meristems fail to form flowers but keep the “memory” of their transient passage in a floral state. Additional mutations affecting meristem growth can induce the production of conical structures reminiscent of the conspicuous fractal Romanesco shape. This study reveals how fractal-like forms may emerge from the combination of key, defined perturbations of floral developmental programs and growth dynamics.

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