Is That a Fibonacci Blooming in Our Yard?

Purple columbine blossoms in our rock garden in spring. A fibonacci number expressed. Photo by Barbara Newhall

Columbines nod their symmetrical heads in our rock garden. Actual flowers? Or just a bunch of fibonacci numbers? Photo by Barbara Newhall

By Barbara Falconer Newhall

Is ours a strictly mathematical universe? Are those stems, leaves and buds pushing up out of the dirt in our front yard no more real than so much digital code, a string of fibonacci numbers? A recent NOVA segment, “The Great Math Mystery,” suggests that maybe that outrageously purple columbine blossom bobbing in a summer breeze out there in our rock garden right now is no more real than a series of mathematical equations.

California native blue-eyed grass, small blue flowers. Fibonacci numbers. Photo by Barbara Newhall

California native blue-eyed grass. Six petals each. Photo by Barbara Newhall

Just a Computer Game?

It’s as though we’re all living inside a computer game where creation is all math and no substance, Max Tegmark of MIT opines. Math doesn’t just describe reality; it is its essence. “Mathematics is all that there is,” he says. “There is nothing else. Math actually is our physical reality.”

Nature gets its shape from a mathematical ordering of things, the NOVA segment goes on to explain. A nautilus shell, for example, is ordered by a progression of fibonacci numbers, in which each number is the sum of the previous two.  Like this: 0, 1, 1, 2, 3, 5, 8, 13, 21 . . .  Measure the swirling, ever widening dimensions of that nautilus shell and they progress just like fibonaccis.

So, I’ve got to ask myself, are those columbines nodding so serenely in the summer breeze for real? Or are they just so many digital fibonacci numbers working their will upon my digital psyche?

A Columbine or a Fibonacci?

Camellias, isotomas, and the columbine descendants of the plants my friend Bob Rothe put in thirty years ago — they emerge every spring in our garden from mud, manure, leaf rot, earthworms and sow bugs. They take in water and sun. And here they are again — with their intricate lines, dewy textures, and colors beyond naming. Also their precise, mathematically predetermined arrangement of sepal and petal. How do they do it?

Could it be that, when I’m out in the garden, kneeling over our tenth generation columbines, getting up close with those deep purple petals — could it be that I’m witnessing fibonacci numbers in action and not an actual swirl of petals.

It might be. But that begs the deeper question — how in the world do earthworm castings become a petal and a leaf? It’s amazing.

Is there a fibonacci sequence for amazement?

More floral amazement at “The De Young Is Bursting With Art — And Flowers.”  More beauty at “Beauty — What to Do About It.”

Two ants investigate a white camellia blossom, both blossom and ants illustrate the principle of fibonacci umbers. Photo by Barbara Newhall

Two ants investigate a camellia; both blossom and ants express fibonacci numbers. Photo by Barbara Newhall





  1. My brainy nephew has this to say about fibonaccis:

    When you ask whether you’re witnessing “Fibonacci numbers in action and not an actual swirl of petals”, I would say No, you’re witnessing both! A swirl of petals IS Fibonacci numbers in action!

    If you want a nice visual illustration of the beauty in math, look at the Mandelbrot set.

    Here’s a cool fact. put the Fibonacci numbers behind the decimal point, sliding each one to the right like so:


    and so on, forever. When you add these all up, you get an EXACT answer of 1/89. It’s interesting to note that 89 is itself a Fibonacci number.

  2. ginger rothe says:

    you made me laugh, and think.

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