Why Are Cauliflowers So Mathematically Beautiful? A New Study Has The Answer


Dr. Katie Spalding


Dr. Katie Spalding

Freelance Writer

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory.

Freelance Writer


Tasty on a fractal level. Image credit: MPH Photos/Shutterstock

If somebody asked you for a real-world example of transcendent mathematical beauty, it’s unlikely you’d reach for the vegetable drawer.

But if, in a moment of domestic self-reflection, you ever find yourself gazing into a head of cauliflower, you might be surprised at what you find. Hundreds of spirals of all different sizes form the florets of the vegetable, all of them replicas of each other. And the closer you look, the more intricate the pattern becomes.


These kinds of patterns are called fractals, and they can be found just about everywhere: from the littorally unending to the literally mindbending. As we’ve already seen, they can even turn up in the produce aisle. But there’s something particularly special about the cauliflower – and a new study published today in Science now has an explanation for it.

If you’ve ever looked at a sunflower, or a pinecone, or cactus, or really most any plant, you may have noticed that the petals seem to spiral out in a particularly satisfying way. Scientists have puzzled over just why this happens for more than two millennia, and they’ve come up with some pretty amazing explanations for the phenomenon over the years.

But cauliflowers, with their nested spirals repeated over many scales, have remained elusive – so elusive, in fact, that today’s study originated twelve years ago. That’s right: the vegetable you thought was just broccoli’s more pale cousin took over a decade to decode.

The clue came from a plant called Arabidopsis thaliana. It’s just a weed – you may even have it in your own backyard – but it’s important for two reasons. First, it’s been studied extensively, so there’s a lot of information out there about it. Second, it’s a brassica – just like cauliflower. That meant that by comparing the genetic makeup of Arabidopsis with a computer-generated model of a cauliflower, the team could figure out what was going on.


Now, while fractals in math repeat themselves forever, in the real world there’s a limit on how small things can get. When you look at a cauliflower, you can see the spirals getting tinier, but just how far down does this self-similarity go? You might be surprised to learn that the first spiral in every plant is actually microscopically tiny, and it governs precisely how the rest of the plant will grow via specific gene expressions.

“The genes expressed in a spot determine whether this spot will grow into a branch, a leaf or a flower,” study co-author Etienne Farcot wrote in a piece for The Conversation. “But the genes are actually interacting with each other, in complex “gene networks” – leading to specific genes being expressed in specific domains and at specific times.”

Farcot explained that there are four main genes that govern how a plant will develop: “their initials are S, A, L and T, which we obviously joked about,” he said. But in cauliflower-like Arabidopsis plants, one of these genes is missing: the “A” gene. Normally, this is the gene that triggers the development of flowers, so its absence explains why the vegetables are notably more “cauli” than “flower”.

But just because a cauliflower can’t grow actual flowers doesn’t mean it won’t try – and that’s how it grows its distinctive fractal geometry. Instead of being able to grow flowers, the spiral can only develop a stem, Farcot said, which in turn develops a stem, and so on until eventually a cauliflower is formed. Leaves and flowers cannot be grown, and so we are left with these layers upon layers of intricately spiraling cauliflower buds.


“It is amazing how complex nature is,” concluded Farcot. “The next time you have cauliflower for dinner, take a moment to admire it before you eat it.”



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  • tag
  • genetics,

  • plants,

  • mathematics,

  • fractals,

  • weird and wonderful,

  • cauliflower,

  • brassica