Of flowery heads and heady maths

Keep your face to the sunshine
and you cannot see the shadow.
It’s what sunflowers do.”
~ Helen Keller

sunflowerField

 The monsoon had set in but so had the colours. We got our share of both during one of our recent trips towards the Western Ghats. On either side of the road was a bed of sunflowers. The skies were grey, the monsoon on a high, but the brightness never ceased. There was no sunshine, but the rains, the greens and the yellows were a joy to behold.

What Helen Keller said is a beautiful thought – but when I read more about sunflowers, I understood that it was only the buds that track the Sun. This tracking, where the plant parts move in response to the direction of the Sun, is called Heliotropism. This motion continues till they are buds and stops when the flower is fully developed and it remains facing East. Now, I wonder if Helen Keller really did address this to adults, asking them to continue what they did when they were ‘buds’ 😉

sunflowerCentre

The sunflower is cultivated in rainfed areas, during the Kharif/Rabi season, sown more between August and October. (Kharif refers to sowing, cultivating and harvesting during monsoon, while Rabi crops are winter crops).  If lotus is the king of flowers, the sunflower is a flower of flowers – not just because it is beautiful, but literally. The sunflower belongs to the family Asteraceae, which gets its name from Aster, which means ‘star’. The main feature of this family is that the mature flower is actually a composite of several flowers, and hence, flower of flowers! This grouping of several flowers is called inflorescence and the adult flower is actually a ‘flowery head’. The same is true for other members of this family like asters, daisies and other kinds of sunflowers.

beeAndPollen

I got closer to the flowery head, keeping my distance so that the bee goes about its work.  Sunflowers are pollinated by honey bees (Apis species) and non-Apis bees (wild bees). What a lot of pollen it was carrying! It was a lovely sight. I got lost watching the bees flying from flower to flower. When one of them vacated their ‘feeding site’, I decided to go closer. The pattern was mesmerizing. This was the composite, the group of florets (small flowers).

Vogel'sModel

It took me back to the days when I would spend hours with my spirograph, sometimes with one color, sometimes with more.  H. Vogel proposed a model for the pattern of florets, known as Vogel’s model. To put it in brief, each floret is oriented towards the next at 137.5°. The number of left spirals and the number of right spirals are Fibonacci numbers. In a typical sunflower, there are 34 in one direction and 55 in the other. Here is a link where you can click on an animation that highlights the right and left spirals.

Dizzy? 🙂 I am. This pattern apparently ensures that the seeds are packed efficiently in the flowery head.  Check out this video for Vogel’s model.

bud


Asters and daisies have their Fibonacci connection too, with the number of petals. Here are some photos of asters, with and without petals.

red

aster

asterPurple

This also reminds me of a visit to The National Gallery, London. A couple of my favourite paintings were by Canaletto and “The Ambassadors” by Hans Holbein the Younger.

VanGogh

Rana’s favourite was Van Gogh’s Sunflowers. Here is a replica, decorating our wall:

These are just a couple in the millions of patterns in nature. It is fascinating. If only everything could be left as is…

References:

Sugandhi

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18 Comments

  1. Thishya said,

    September 4, 2013 at 8:34 pm

    Nice post 🙂

  2. Vaidy said,

    September 5, 2013 at 4:54 am

    Interesting One 🙂

  3. hrao said,

    September 5, 2013 at 6:49 am

    Amazing patterns!! Thanks for sharing interesting information on floret models!!

  4. September 5, 2013 at 7:31 am

    wow…lovely information..tfs….

  5. Sudhindranath said,

    September 5, 2013 at 12:18 pm

    some thing which you never observe when you see sun flower.the observation is great and is eye opener,
    surabe

  6. A K Prabhakara said,

    September 6, 2013 at 2:38 am

    Excellent observations- Fibonacci number and Vogel model. Carry on the exploration of mysterious link between nature and maths.

  7. Ramya said,

    September 6, 2013 at 9:35 am

    Wow! Very interesting.

  8. deponti said,

    September 11, 2013 at 3:02 pm

    A lot of interesting information! thank you!

    deepa.

  9. Ravi Maganti said,

    October 8, 2013 at 6:12 pm

    Keep it coming! very nice read.


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