What makes Romanesco broccoli so mathematically perfect?



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In terms of taste, broccoli is a vegetable that divides. But visually, you’d be hard pressed to find anyone who doesn’t find Romanesco broccoli aesthetically beautiful.

You’ve probably stopped to look at it in the produce aisle: Romanesco broccoli – or “Romanesco” for short – is a breed of broccoli that looks like a giant green flower, with strangely perfect geometric patterned flowers that repeat as you zoom in. It is the nautilus shell of vegetables: a perfect spiral, always repeating, which resurfaces again and again. As a late fall and winter vegetable, it can be found in most grocery stores in the United States at this time of year, mesmerizing shoppers with its stunning patterns.

These patterns are called fractals and are essential to understanding Romanesco broccoli.

“A fractal is a shape or structure identical to itself at different scales,” wrote Edmund O. Harriss, professor of mathematics at the University of Arkansas, in Salon. “In other words, when you zoom in, you see the same structure (or sometimes linked).”

In the natural world, plants sometimes come close to these self-repeating structures. Many ferns, for example, have leaves that feature fractal architecture. Pine cones, spiral nautilus shells, and ice crystals also have self-repeating patterns.

But among the recursive patterns that appear in living things, Romanesco broccoli is a fractal ultimate, it seems.

“Romanesco is considered to be the model par excellence of fractal architecture in biology”, Zachary Stansell, a professor at Cornell University’s School of Integrative Plant Science, told Salon via email. “We know that it exhibits a very unusual and recursive growth pattern compared to ‘normal’ (or Calabrese) broccoli. Almost paradoxically, some of the rules that govern normal branching and development of broccoli appear to be ‘relaxed’ in Romanesco. – which allows him to repeat the process of branching … over and over. This iterative branching model corresponds to interesting mathematics like the golden ratio, a common theme in classical architecture. “

One of the oldest mathematical concepts, the golden ratio, the value of which is around 1.618, is the ratio between two objects of different size in which the smaller is the larger and the larger is the sum both. As John Edmark, professor in the mechanical engineering and design program at Stanford University, told Salon, the golden ratio happens “if you take a line and divide it into two segments so that the ratio of the entire line to the longest segment is the same as the ratio of the longest segment to the shortest segment. ”Edmark noted that“ there is only one ratio that can meet this requirement – the Golden Ratio – and its value is approximately 1.618. “

The golden ratio has a rich history, dating back to the ancient Greek mathematician Euclid. It has been used by artists, architects, engineers and musicians, incorporated into their respective trades. Some even believe that it can be used to explain beauty and understand how life is conceived in nature.

This brings us back to Romanesco broccoli. The spiral pattern on broccoli features the golden ratio, in that each little bud that grows outward from the main has the same size ratio as its predecessor, especially the golden ratio. In other words, the same formula that governs the appearance of Romanesco broccoli was exploited by Leonardo da Vinci and Piet Mondrian in their canvases.

That’s the math behind the broccoli. But what about biology? What about Romanesco’s genetics that make him so … spiraling?

Oddly enough, why Romanesco is different from its almost genetically identical cousins ​​- (normal) broccoli and cauliflower – remains a genomic mystery.

“To my knowledge, no one has fully proven the genetic control of the patterns seen at Romanesco,” Stansell told Salon. “There are known genes in the ‘lab rat’ of plants (Arabidopsis thaliana) which appear to induce somewhat analogous behavior, but genetic control remains an ongoing issue. “

Thomas Björkman, colleague of Stansell Cornell, added to these observations, writing to Salon that “broccoli (like cauliflower) is built by the growing point making branches and flowers in a cohesive repeating pattern. On the other hand, Romanesco’s more regular appearance is caused by the growing point made of branches and flowers in an ever-changing pattern. In Romanesco, the time and distance between new branches keep getting longer. you look at the tip of a Romanesco’s head, you will see that the growing point is really large, easily visible to the naked eye. “

Stansell and Björkman know what they’re talking about when it comes to broccoli, because the two scientists published a paper in October on the genetics of broccoli. They studied the genomes of broccoli and learned that the iconic plant has retained about half of the genetic diversity that existed in the original broccoli cultivated by Italians centuries and centuries ago – information that could be used to change its taste in the future.

“Even though modern broccoli is extremely uniform, it retains about half of the genetic diversity found in its Italian ancestors,” Björkman explained. “This diversity is valuable for resilience and continuous improvement.”

He added that he and his co-author, Stansell, “have also found parts of the genome (the body’s entire set of genetic instructions) where genetic diversity is really low. This uniformity is a sign that there is a gene in that part of the genome. is really important to making good broccoli and the other versions have been eliminated. “This reveals that people who grew broccoli deliberately knew which traits to encourage and which to minimize. Interestingly, this happened thanks to the farmers who grew the vegetable, long before humans even understood that genes existed.

The “distinctive flavor” of brassica vegetables, the cabbage and mustard family in which broccoli is also found, relates to a class of compounds called “glucosinolates,” Stansell told Salon. “Certain glucosinolates contribute to the spicy or bitter flavors that people love (or hate) in broccoli,” he noted.

Stansell also observed that human genetics may play a role in how we understand the relevance of broccoli genetics; some people have genes that make them more sensitive to glucosinolates.

“It’s possible to breed brassica vegetables to have less of these bitter compounds, like Dutch breeder Hans van Doorn did when breeding Brussels sprouts,” Stansell explained. “A better understanding of the genetic diversity of broccoli could allow plant breeders to select or pollinate new varieties of broccoli with different or even new flavor profiles.”

Perhaps, in time, such genetic knowledge could also enable breeders to select mathematically amazing broccoli.

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