Monks once hoped to turn lead into gold through alchemy. But consider the cauliflower instead. It takes just two genes to transform the ordinary stems, stalks and flowers of the weedy, tasteless species Brassica oleracea into a formation as marvelous as this fractal, cloudlike vegetable.

This is the true alchemy, says Christophe Godin, a senior researcher at the National Institute for Research in Digital Science and Technology in Lyon, France.

Dr. Godin studies plant architecture by virtually modeling the development of the forms of different species in three dimensions. He wondered what genetic modification lurked behind cauliflower’s nested spirals and the logarithmic chartreuse fractals of Romanesco, a cauliflower cultivar that could almost be mistaken for a crystal.

“How is nature able to build such unexpected objects?” he asked. “What can be the rules behind this?”

Fifteen years ago, Dr. Godin met François Parcy, a plant biologist with the National Center for Scientific Research in Grenoble, France. In Dr. Parcy, Dr. Godin recognized a fellow fiend for fractal florets.

“There is no way you cannot notice it is such a gorgeous vegetable,” Dr. Parcy said, in reference to Romanesco.

Buoyed by a passion for Brassica, Dr. Godin and Dr. Parcy investigated the genetic mystery of the fractal geometry in both Romanesco and standard cauliflower, conjuring the plants in mathematical models and also growing them in real life. Their results, which suggest the fractals form in response to shifts in the networks of genes that govern floral development, are published Thursday in Science.

“It’s such a nice integration of genetics on one hand and rigorous modeling on the other,” said Michael Purugganan, a biologist at New York University who was not involved with the research. “They’re trying to show that by tweaking the rules of how genes interact you can get dramatic changes of a plant.”

In the early 2000s, Dr. Parcy believed he understood the cauliflower. He even taught classes on its flower development. “What is a cauliflower? How can it grow? Why does it look like this?” he said.

Cauliflowers, like brussels sprouts, stem from centuries of selective breeding of Brassica oleracea. Humans bred brussels sprouts for lateral buds and cauliflower for flower clusters. Cauliflowers, however, do not produce flower buds; their inflorescences, or flower-bearing shoots, never mature to produce flowers. Instead, cauliflower inflorescences generate replicas of themselves in a spiral, creating clusters of curds like plant-based cottage cheese.

As the two researchers discussed cauliflower, Dr. Godin suggested that if Dr. Parcy truly understood the plant, it should be easy to model the vegetable’s morphological development. As it turned out, it was not.

The two first confronted the curdled quagmire on the blackboard, sketching out various diagrams of genetic networks that could explain how the vegetable mutated into its current shape. Their muse was Arabidopsis thaliana, a well-studied weed in the same family as cauliflower and its many cousins.

If a cauliflower has a single cauliflower at the base of the plant, Arabidopsis has many cauliflower-like structures along its elongated stem. But what genes could refine these lesser cauliflowers into one grand, compact cauliflower? And if they identified those genes, could they warp these cauliflowers into the peaks that Romanescos form?

To answer these questions, the researchers would tweak the gene network and run it through mathematical models, generate it in 3-D and mutate it in real life. “You imagine something, but until you program it you don’t know what it’s going to look like,” Dr. Parcy said.

(Over the course of the research, Dr. Parcy also collected several specimens of Romanesco from his local farmer’s market, sequenced and dissected them. He and his colleagues then dined on the leftovers, most often raw with different dips, along with glasses of beer.)

Many initial models flopped, bearing little resemblance to cauliflowers. At first, the researchers believed the key to cauliflowers lay in the length of the stem. But when they programmed Arabidopsis with and without a short stem, they realized they did not need to reduce the stem size of the cauliflowers, either in the 3-D models or in real life.

And the cauliflowers they simulated and grew were simply not fractal enough. The patterns were visible only at two fractal scales, such as one spiral nested in another spiral. By contrast, a regular cauliflower often displays self-similarity in at least seven fractal scales, meaning a spiral nested in a spiral nested in a spiral nested in a spiral nested in a spiral nested in a spiral nested in, ultimately, another spiral.

So instead of focusing on the stem, they concentrated on the meristem, a region of plant tissue at the tip of each stem where actively dividing cells produce new growth. They hypothesized that making the meristem bigger would increase the number of shoots produced.

The only problem was that the researchers did not know what gene might control the meristem’s pace of shoot production.

One day, Eugenio Azpeitia, then a postdoctoral fellow in Dr. Godin’s lab, remembered a gene that was known to change the size of the central zone of the meristem. The three researchers enjoyed a brief moment of euphoria, and then waited patiently for months for their newly modified Arabidopsis to grow. When the shoots sprouted, they had cauliflowers with distinct conical tips.

“Very reminiscent of what occurs in the Romanesco,” Dr. Godin said proudly.

Normally, when a plant sprouts a flower, the flowering tip of the plant prevents more growth from the stem. A cauliflower curd is a bud that was designed to become a flower but never makes it all the way there, and instead makes a shoot. But the researchers’ experiments in the meristem found that because this shoot has passed through a transient floral stage, it is exposed to a gene that triggers its growth. “Because you have been a flower, you are free to grow and you can make a shoot,” Dr. Parcy said.

This process creates a chain reaction where the meristem is creating many shoots that, in turn, creates many more shoots, enacting the fractal geometry of a cauliflower.

“It’s not a normal stem,” Dr. Godin said. “It’s a stem without a leaf. A stem with no inhibition.”

“That’s the only way to make a cauliflower,” Dr. Parcy said.

The researchers say there are likely other mutations responsible for the spectacular shape of Romanesco. Ning Guo, a researcher at the Beijing Vegetable Research Center who is also studying the potential genetic mechanism behind the architecture of the cauliflower curd, says the paper has offered “a lot of inspiration.”

“The story is not yet finished,” Dr. Godin said, adding that he and Dr. Parcy will continue refining their cauliflower models. “But we know we are on the right track.”

But they are open, they say, to studying anything that flowers.

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