Romanesco Broccoli: A Fibonacci Fractal

Romanesco broccoli florets

Few things in the garden are more mesmerizing than the Italian heirloom brassica of Romanesco broccoli.

This chartreuse bud is an edible flower that is also known as a Romanesco cauliflower, but it’s technically neither — truly in a class of its own. It’s a fine work of art and a mathematical marvel. Did you know that a Romanesco is a beautiful example of a Fibonacci fractal in the natural world?

Last year I picked my Romanesco a few days too late, and its famous spiral had already started to unravel, resembling an average cauliflower. But this year, I remembered to harvest it earlier (and thankfully, it weighed much less than the 25-pound Broczilla from last year’s crop!).

The part of the broccoli that we typically eat — what we call the head — is actually the flower bud of the plant (although broccoli leaves are just as edible and delicious, and can be cooked like any other green). The tight clusters that form the head are called florets (or small flowers).

Romanesco broccoli fractals

On a Romanesco, the whole head is made up of smaller heads that mimic the shape of the larger head, and each of those smaller heads is made up of even smaller, similar heads. It keeps going, and going, and…

You’re looking at a natural fractal — quite simply, a detailed pattern that repeats itself ad infinitum. (But since a head of broccoli can’t go on forever, math purists would call this an approximate fractal, since it has a termination point.) If you break off a floret, it looks like a mini broccoli with its own mini florets. Fractals are fascinating in that way; no matter which part of the fractal you zoom in on, it will be an identical version of the bigger picture.

Romanesco cauliflower florets

A head of Romanesco broccoli

If you ever have the chance to study a tight head of Romanesco up close, you’ll see a spiral emanating from the center point, along which all the smaller florets are arranged. This is the Fibonacci spiral, a series of arcs whose radii follow the Fibonacci sequence. You remember the Fibonacci sequence from school? Where each number equals the sum of the previous two numbers? 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

If you count the number of spirals in one direction, and then count the number of spirals in the other direction, they will be — without fail — consecutive Fibonacci numbers. Every time. Intrigued? Confused yet? I know I was. I’ll let this math geek explain it better with a visual.

If you don’t have a head of Romanesco to test out this mathematical wonder, try it with other self-similar forms; cauliflower, sunflowers, pinecones, and pineapples are all examples of Fibonacci spirals.

Isn’t it amazing how something so precise as a math formula can occur in something so organic as a head of broccoli?

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April 25 2012      19 comments     Linda Ly
Jardín   Verduras

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  • Jake Witmer

    Excellent site! Very nice dedication to healthy and useful environment, and all the wonderful nanotech that nature and evolution selected for us. This information is excellent. I’ll be checking out your site to see if and when you start growing all of the recommendations of Paul Stamets on youtube. Definitely check out his TED talk, if you haven’t already. He shows how you can grow many kinds of cancer and heart-disease preventing mushrooms that also “close the nutrient loop” in your vegetable garden, making your vegetables grow much more vigorously, and contributing more to their chemical nutrient profiles.

    • Linda Ly

      Thanks. I’ve always been fascinated by mushrooms and hope to learn more about them one day.

  • Pingback: 2012: A Year in Review | Garden Betty()


    just tried one. Lovely!

  • Ronda

    I love your explanation of the Fibonacci sequence.  I read an article about it once and now I always see it in my garden, usually in the sunflowers. I think the article I read was in an “Awake!”  magazine. It also mentioned that seashells display the same pattern.  Just stumbled on your blog looking to see if I should eat the leaves of my broccoli that got started too late and didn’t produce heads.  Thank you for the info!  I’ll enjoy the rest of your site now and I’m going to bookmark it!

    • Linda Ly

      I love seeing the spirals in my Lemon Queen sunflowers!

      Thanks for reading!

      • reza

        hi dear linda
        i’m reza from iran i live in the north
        i’m biotechnologist i have a farm that plant broccoli in it

        like you i love to grow something that can make happy the peaple

        • Linda Ly

          Gardening is one of the greatest forms of therapy. 🙂

  • bria Phillips

    Wow, you are a cruciferous rock star!  I’ve tried to grow them so many times, including the beautiful romanesca, but am always plagued by pests that I’ve given up.

    • Linda Ly

      I grow a lot of beneficial plants in the garden, so I don’t see as many pests anymore. Sluggo Plus and food-grade diatomaceous earth also work great, depending on what’s plaguing your garden. You can even try floating row covers to keep cabbage worms and other pests off your plants.