• Seeing Nature’s beauty in numbers

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    Why are there patterns in Nature?

    ‘We are guided by nature in composition’

    Down from the top of the drive where he goes to get the daily paper, my husband, Tractor Man, brought me a thistle flower.

    Very pretty, I love it! …I’m afraid it’s an invasive bull thistle, though, not the one it reminds me of… the lovely California native Cobweb thistle in the photo below, Cirsium occidentale, written up by gardening friend, Town Mouse, here.

        California Thistle, Cirsium eriophorum, Wikipedia

    California Thistle, Cirsium eriophorum, Wikipedia

    The thistle bud Town Mouse posted has a design that makes me think 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.

    — If you don’t like science and math, skip to the beautiful photos and to the amazing video! —

    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 seed head, you would find that they are two neighboring numbers in this sequence, most commonly 55 and 89. Interesting?

    It’s amazing to me that mathematicians would be able to describe the appearance of certain 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 that 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.


    Nature’s spirals in plants

    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.  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.”

    Fascinating sunflower spiral patterns

    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?  ~~ Sue


    Sunflower by Sue Langley


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    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 manages the Flea Market Gardening Facebook page and website.


    1. Nell Howard Stelzer says:

      That was very interesting and I have never gave a thought to mathermatics in it. I love to capture the patterns in photos of plants,flowers and nature at it’s best. Thanks for sharing this and bringing it to my attention !!

      1. Sue Langley says:

        It’s fun to see things from a little different perspective,..makes you really pay attention. Fun!