• Seeing beauty in numbers

    by  • June 6, 2011 • Design, Garden art • 2 Comments

    ‘We are guided by nature in composition’
    Bartók

    Down from the top where he goes to get the paper, my husband brought me a thistle
    flower. Very pretty, I love it! …I’m afraid it’s a bull thistle, not the lovely California native Cobweb thistle, Cirsium occidentale, written up by Town Mouse, here.

    California Thistle, Cirsium eriophorum

    California Thistle, Cirsium eriophorum, Wikipedia

    The thistle bud Town Mouse posted has a design that reminded me of the Fibonacci sequence of numbers, a mathematical theory that applies to, among other things,  patterns in nature. It shows up in the number and positions of the petals, leaves, and seeds in plants.

    What is the Fibonacci sequence?
    Each number in the sequence is determined by adding two numbers together starting with 0: 0+1 = 1, 1+1 = 2, and so on. Numbers of seeds and petals appear in this sequence or in these particular numbers in many plants. These are the first few Fibonacci numbers most commonly found in flowers and many other things in nature.

    — 1  2  3  5  8  13  21  34  55  89  144  233  377  —

    In a thistle head above, some spirals go clockwise, and some counter-clockwise.  If you count, there are thirteen spirals going clockwise, and twenty-one counter-clockwise, 13 and 21, two numbers in the sequence.

    Should you count the number of spirals in the sunflower seedhead, you would find that they are two neighboring numbers in this sequence, most commonly 55 and 89.

    It’s amazing to me that mathematicians would be able to describe the appearance of the plants with this group of numbers. Not all plants can be described this way, but isn’t it interesting and beautiful, these patterns?

    Sunflower pattern showing spirals

    Sunflower pattern showing spirals

    The main reason I wanted to do this post is to show this 3 1/2 minute video inspired by numbers, geometry and nature, by Cristóbal Vila, and while not all the numbers add up, it’s beautiful to watch.

    Once I became aware of this theory, (which by the way occurs in the dubious, but entertaining movie, ‘The Da Vinci Code’), I began to notice more patterns that applied. Pine cones, asparagus, some succulents, vegetables like broccoli and cauliflower and Town Mouse’s thistle!

    If you count the number of petals in this succulent, it will be a Fibonacci number

    If you count the number of petals in this succulent, it will be a Fibonacci number

    Observing design in nature has been an influence on me when it comes to art, photography and the natural world. I’m so fascinated in the patterns and designs in nature and many of my photos reflect that.  It’s a joy to me that is deeply satisfying. The Fibonacci theory gives an explanation for why such designs exist, in other words, whatever is the reason for the designs and patterns to be there.

    One reason is optimal packing. The more seeds a plant has, the better the survival rate. Each seed has enough room to develop. This works for, say, the sunflower, because of how it grows from the center of the seed head, each seed at a particular mathematical angle, pushing the outer seeds further out.  This creates enough space for each to develop, whether in the middle or on the edge. Any advantage like this over the eons contributes to a plants survival. Plants don’t know any of this — they just grow in the most efficient way.

    Pine cone spirals according to numbers

    Pine cone spirals according to numbers

    Nature also causes leaves to grow in a spiral around the stem, most likely to allow each to have sun. Those patterns can be described by the smaller numbers in the Fibonacci sequence. There is a whole field, called phylotaxis, which is the study of the ordered position of leaves on a stem. While every flower doesn’t show this perfect formula, you can see the sensibility, and the beauty.

    Can you see the spirals in this Romanesco broccoli?

    Can you see the spirals in this Romanesco broccoli?

    Why does math have anything to do with plants?  It’s sort of an elegant and beautiful ‘form follows function’ situation. The science website, Brantacan, says,

    “The rule is that the leaves or florets grow for maximum space.  The rest –
    Fibonacci numbers, spirals, pretty patterns – follows automatically.”

    Sunflower seeds, beautiful patterns, but no time to count them...I'll take your word...

    Sunflower seeds, beautiful patterns, but no time to count them…I’ll take your word…

    Recognizing organized shapes and patterns is an orderly, calming and beautiful way to perceive nature and I’m delighted when I can see them in my world. Do you see design in nature?

    Notes:
    Amazingly, the family trees of male honeybees have to do with the Fibonacci sequence. The link goes to a slightly sleep inducing video, but it’s also an interesting phenomenon.
    The theory behind this movie
    Mr. Vila does have a disclaimer about the nautilus in the film saying that it doesn’t exactly correspond, which found out about after he made the movie…(darn!)
    Who was Fibonacci?
    Fibonacci Flim-Flam  – this somewhat fussy website cautions against the idea the there is mysticism or magic in Fibonacci’s numbers. He points out inaccuracies in some examples including the nautilus.
    More than you want to know about the Fibonacci sequence
    Petals on flowers
    Seedheads This part has neat animations showing the spirals
    Pinecones
    Leaf arrangements here’s more info on Phylotaxis
    Vegetables and Fruit

    About

    Sue Langley, a passionate gardener and photographer lives and gardens with her husband and Corgi, Maggie on 7 acres just south of Yosemite, Zone 7 at 3000 feet. She also manages the Flea Market Gardening Facebook page and website.

    2 Responses to Seeing beauty in numbers

    1. June 7, 2011 at 5:32 pm

      what a fascinating post…love when we can discover the math in nature…I definitely have to share this post with a math teacher friend..she would love it as did I…

    2. June 7, 2011 at 9:41 pm

      Fun and interesting post. I love the Bartok quote, and he didn’t just say it, he actually composed with the Golden Mean to structure some of his pieces (e.g. the Music for Strings, Percussion and Celesta which I dearly love). And Fibonacci numbers were hot with a couple of student composers in my grad school days. I never used them for music, but one of my first projects around the house was a segmented concrete walkway divided down the middle, where the sizes of the segments on one side increased according to the Fibonacci sequence, while those of the second side used decreasing Fibonacci numbers. Unfortunately the walkway didn’t survive a remodel and is now history.

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