What fractals, Fibonacci, and the golden ratio have to do with cauliflower

Macro-photo of green Romanesco cauliflower showcases the vegetable's striking fractal pattern.

Enlarge / Macro-photo of green Romanesco cauliflower showcases the vegetable’s striking fractal pattern. (credit: Cathy Scola / Getty Images)

It’s long been observed that many plants produce leaves, shoots, or flowers in spiral patterns. Cauliflower provides a unique example of this phenomenon, because those spirals repeat at several different size scales—a hallmark of fractal geometry. This self-similarity is particularly notable in the Romanesco variety because of the distinctive conical shape of its florets. Now, a team of French scientists from the CNRS has identified the underlying mechanism that gives rise to this unusual pattern, according to a new paper published in Science.

Fractal geometry is the mathematical offspring of chaos theory; a fractal is the pattern left behind in the wave of chaotic activity. That single geometric pattern repeats thousands of times at different magnifications (self-similarity). For that reason, fractals are often likened to Russian nesting dolls. Many fractal patterns exist only in mathematical theory, but over the last few decades, scientists have found there are fractal aspects to many irregular yet patterned shapes in nature, such the branchings of rivers and trees—or the strange self-similar repeating buds that make up the Romanesco cauliflower.

Each bud is made up of a series of smaller buds, although the pattern doesn’t continue down to infinitely smaller size scales, so it’s only an approximate fractal. The branched tips, called meristems, make up a logarithmic spiral, and the number of spirals on the head of Romanesco cauliflower is a Fibonacci number, which in turn is related to what’s known as the “golden ratio.”

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