Succulents, Fibonacci and Spiral Phyllotaxis

Many cacti and succulents form geometric spirals similar to those of sunflowers, pine cones and nautilus shells. Spiral leaf arrangements funnel rain to roots, and keep upper leaves from shading lower ones.

The arrangement of a plant's leaves along the stem is phyllotaxis (from ancient Greek, phýllon "leaf" and táxis "arrangement"). Mathematically, spiral phyllotaxis follows a Fibonacci sequence, such as 1, 1, 2, 3, 5, 8, 13, etc. Each subsequent number is the sum of the two preceding ones.

There's a hypnotic beauty about spiral phyllotaxis, not to mention it's a great phrase to impress friends with. As is the puzzling-to-pronounce Fibonacci (fee-bo-NACH-ee), the name of a 12th-century Italian mathematician.

Perhaps the best known succulent to do this is aptly name spiral aloe (Aloe polyphylla). Unfortunately it's devilishly tricky to grow, making it the Holy Grail of succulents. (If you can grow a spiral aloe, you can grow anything.)

Aloe polyphylla, also known as Spiral Aloe

I'm fond of spherical cacti because of how their spines spiral---in fact, I almost prefer the plants out of bloom. These are mammillarias. I show a cool way to display them in another article, Create a Cactus Curio Box. And I describe the growing popularity of these photogenic plants in Is Cactus the New Black?


Sempervivum arachnoideum, cactus spiral

Sempervivum arachnoideum, cactus spiral

Sempervivums (hens-and-chicks) also spiral beautifully. Squint at this photo and you'll see how similar it is to the center of a sunflower.

Sempervivum arachnoideum, cactus spiral


Medusa euphorbias, known for their craggy, snakelike stems, each has a spiral at its center. No two are the same, and seldom do you find one that's perfect.

Medusa euphorbia


Have you noticed spiral phyllotaxis in your own garden? Do look for it. You may be surprised at how it jumps out at you, once you're aware of it.


Debra Lee Baldwin, Garden Photojournalist, Author and Succulent Expert

Learn more about Debra Lee Baldwin, garden photojournalist, author and succulent expert



Cactus snowflake

How Cactus Snowflakes Seduced Me

Remarkably, the spination of certain cacti suggests snowflakes, something I first noticed years ago at a succulent specialty nursery. I was there to photograph aloes in bloom, but I’d come too early in the season. I thought of leaving, and I’m so glad I didn’t! That afternoon forever changed the way I see certain succulent…

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  1. Sylvia McMaster on October 29, 2019 at 4:30 pm

    Debra, Thanks so much for showing us such unusual succulents. Wow! isn’t creation amazing! I love that growers find ways to cultivate such beauties and thank you for sharing the pictures with us. I love succulents and the rare’er the better. I enjoy reading your newsletter every week I learn something new from it.

    • Debra Lee Baldwin on October 29, 2019 at 7:34 pm

      Thank you, Sylvia. Much appreciated!

  2. Kriti Sodhi on December 3, 2019 at 12:39 pm

    Hi, I am a grade 11 student in Ontario, Canada. I have visited your site many times and have found a lot of very helpful information, specifically related to echeverias. This is because I am conducting a math exploration about the changes of the spiral pattern of two of the same types of echeveria as they grow in two different locations. I would like to gain your insight about this topic as my question is very specific. Do you think the changes in the spiral pattern of either echeveria will be affected if one is put in partial sunlight and the other in direct sunlight? It would be great to get more information for my exploration.

    • Debra Lee Baldwin on December 3, 2019 at 12:52 pm

      Hi Kriti — Echeverias are highly sensitive to light, and in low light will stretch (elongate, or in horticultural terms, etiolate) in the direction of greatest light. Etiolation compromises a rosette’s symmetry, making it lopsided. However, as to “changes in the spiral patterns” I’d have to say no…the patterns would be the same…that is, if you’re referring to the way the leaves emerge from the plant’s central core. That wouldn’t be affected by light. I hope this helps!

      • Kriti Sodhi on December 4, 2019 at 9:07 am

        Yes, it did help! The plant that was placed in partial sunlight did elongate towards the window and became lopsided, however, as you said, it did not affect the central part of the spiral. Thank you so much for your help!

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