Italy, 2023

With its crown of perfectly-formed florets, Romanesco broccoli looks otherworldly — like an AI-generated vegetable. This bright green relative of broccoli and cauliflower is not only tasty with its nutty flavor, it’s also a ripe subject for scientists and mathematicians to research due to its fractal structure, golden ratio spirals, and compact growth pattern.

The structure of Romanesco broccoli is a classic example of a fractal pattern in nature. A fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole — a property known as self-similarity. If you zoom in on one of the buds, you’ll see that it is made up of smaller buds arranged in the same pattern as the whole head. Zoom in again, and you’ll see the pattern repeats itself. Our CT scans use hundreds of 2-dimensional X-ray images to create a 3D model. When we slice this 3D model and scrub up the Z-axis of the Romanesco, we see the fractal burst into fireworks.

Fractals aren’t the only feature of Romanesco that piques the interest of mathematicians. The number of spirals on any given head is also a Fibonacci number. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, 13, 21, etc.). Fibonacci numbers frequently appear in nature, often in structures that grow in a spiral, such as a nautilus shell, a pinecone, or a sunflower. If you count the number of spirals on a Romanesco broccoli in a clockwise direction and then in a counterclockwise direction, the two numbers you get will be consecutive Fibonacci numbers. Divide the larger number by the smaller one, and you’ll get a result close to the golden ratio (approximately 1.61803398875), another mathematical concept that frequently occurs in nature, art, and design.

But how does Romanesco produce these mesmerizing patterns? Our CT software can visualize its density variation with a range mapper, revealing denser areas toward the peak and down in the stem (in red), likely due to compacted cellular structures supporting the growth pattern. Surprisingly, the center appears less dense (yellow and blue), maybe because it serves as a nutrient reservoir for new buds and requires a more porous structure.

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