Wednesday Wonderment – pt 11

Fibonacci is everywhere!

There are certain aspects of Nature that inspire amazement when we look at them and even greater amazement when we analyze them even deeper.

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Fibonacci’s Flower

The mighty sunflower is an amazing little piece of mathematical design, when we analyze the spiral shapes in which the seeds are laid out.  I think most of us have heard of Fibonacci numbers: the sequence 1, 1, 2, 3, 5, 8, and so on, so that each number is the sum of the last two.  When looking at the spiraling shapes in cauliflower, artichoke and the sunflower floret, as seen above, we see this sequence appear in front of our eyes.

Upon analysis, we see that those spirals pack florets as tight as can be, maximizing their ability to gather sunlight for the plant. But how do plants like sunflowers create such perfect floret arrangements, and what does it have to do with Fibonacci numbers? A plant hormone called auxin, which spurs the growth of leaves, flowers, and other plant organs, is the key: Florets grow where auxin flows.  This has been modelled mathematically by researchers to demonstrate the Fibonacci spiral count is the optimal dense-packing strategy.

How to Count the Spirals


The sunflower seed pattern used by the Museum of Mathematics contains many spirals. If you count the spirals in a consistent manner, you will always find a Fibonacci number (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …). Below are the three most natural ways to find spirals in this pattern. Note that the black pattern is identical in all the images on this page. Only the colored lines indicating the selected spirals are different.
The red lines show 34 spirals of seeds.
The red lines show 34 spirals of seeds.
Choosing another slope, the green lines show 55 spirals of seeds.
Choosing another slope, the green lines show 55 spirals of seeds.
And choosing a very shallow slope, the blue lines show 21 spirals of seeds.
And choosing a very shallow slope, the blue lines show 21 spirals of seeds.

– See more about this at: http://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/#sthash.XF0YpZoT.dpuf

Hope you enjoyed this bit of in-depth view of the sunflower!

 

Author: jansenphoto

A Fresh Perspective Photography is more than just a vehicle for capturing the world around me; it provides me with a palette and a set of brushes, with which I paint not only what I see, but also look to express the emotions that are evoked by the scene in front of me in that moment. Growing up in the Netherlands exposed me to a wide cross-section of visual arts that laid the foundation of my photographic view of all that surrounds me. Early influences were the Dutch Masters of the 17th century, to whom I was introduced by my grandfather during museum explorations; favorites among them are the scenes of quotidian life depicted by Jan Steen and Frans Hals and the vivid landscapes of Jacob van Ruisdael. My classical high school education was supplemented by the Boijmans Van Beuningen museum, where I spent many a lunch hour exploring its great collection. Here I was introduced to surrealism with a particular love for the approach taken by Salvador Dali; Dali also rekindled my appreciation for the work of Hieronymus Bosch, who often showed the folly of us mortals. Universal Connections My approach to any photographic subject is to look for understanding first; in this I look to establish either a connection between the viewer and the subject or capture the connection of the subject with its surroundings. The captured image then aims to portray this connection from a perspective that is part of my personal interpretation. This interpretation is often a form of externalized introspection, which may alternately display the connection of isolated beings and items with their environment or highlight the whimsy of the profound world, in which we find ourselves. The universe is full of connections, many of which are waiting to be discovered; part of my journey as a photographer is to document these connections. Any assignment, be it an event, a product shoot or a portrait session is always approached through communication with the client; this is where the first connection is established. Ideas are exchanged and a collaborative plan of action forms, ultimately resulting in a set of images that aim to exceed the expectations of each client. And, lest we forget, it is important to have fun while practicing the serious business of photography!

11 thoughts on “Wednesday Wonderment – pt 11”

  1. Thanks for another great post. I love my sunflowers but have never really looked at them in this way:) I will be looking more closely next season.
    Have a great day

    1. Thank you! Nature is full of interesting patterns that have mathematical properties; it’s part of what makes it very interesting to examine in more detail.

      Have a wonderful day!

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