Saturday, September 12, 2009

Sunflower blooming with precision.

sole surviving sunflower

Finally the sunflower opens up, just about the right size for such one and a half feet height. The flower is so lovely with splashes of yellow. Kakdah was very much excited with the new member of limited flowers in our little vegetable garden. Now we are counting days, how long will the flower be with us, before the seeds are formed and the flower will dry up.

I bumped into a site which explain in great detail the astonishing pattern of florets in the head of a sunflower as proposed by Vogel in 1979.

A model for the pattern of florets in the head of a sunflower was proposed by H Vogel in 1979.[10] This is expressed in polar coordinates
r = c \sqrt{n},
\theta = n \times 137.5^{\circ},
where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. It is a form of Fermat's spiral. The angle 137.5° is related to the golden ratio and gives a close packing of florets. This model has been used to produce computer graphics representations of sunflowers.[11]


Lets appreciate what Vogel tried to arrive at,  about the precision of a sunflower, and lets look at the intricate formation... how delicate....



  1. Wow, you really do have patience to take time to follow these sequences.

  2. So much to learn -- even from the flowers.

    Thank you!

  3. You are really amazing! What attention to detail.

  4. A time lapse view of an incalculable mystery.

  5. This is also Fibonacci sequence. Have a look here/scroll down

    I am still in Friday :)

  6. The awakening of the sunflower. The series of the opening flower is wonderful. On thisandthat I have written about Mathematics in Nature,The Fibonacci Spiral. Thanks for stopping by.

  7. math in the head of a sunflower.....and we think we need science fiction when we have science reality...I am a lover of sunflowers so I found your photos and mathematical equations quite educational....

  8. Your sunflower is blooming like a little girl turning into a gorgeous lady. My sunflower seeds are as dead as a doornail. Still no signs of life yet. Bangchik, what brand of seeds did you use?

  9. Enjoyed the sequences in your photos. Great work. I know about the math and geometry in a sunflower, but it's always to hear about it again. What a wonder.

  10. You did a good job in documenting the growth of your sunflower! As you've said, NEAT! -and really nice!

  11. Hi,
    I am going to sneeze just looking at it. but it is beautiful!!! I love the transitions of watching it open. If it was me, I would have botched it and had it going backwards. I am still figuring out blogger!

  12. Finally the flower opens up, and finally here come your story, that I first come across with a formula.
    And this put pressure on me, where is my equation for my story?

  13. Ooh, Bangchik -- what a neat find about the sunflower pattern! And of course, your sunflower is beautiful. So exciting! Mine opened up yesterday, too -- I'll hopefully have a chance to post a picture today. It's so neat to be able to enjoy the very same progress of our flowers across the world! Makes it seem like such a small world, doesn't it? I'm as attached to your little flower as I am to mine. :)

  14. .


    Understandably, both of us here feel attached with this sunflower. There is reasons to it. Number 1, this is the only one growing after series of failed attempts. Number 2, having a sole survivor around allows us to pamper the little plant a little bit more. I find it necessary at times to look at every leaf shooing ants or insects away!... haha.

    We photographed early in the morning each day. But as it opens up, changes seem to occur every minute!!


    It is good to know more about the equations and mathematics surrounding the mystery of a sunflower. ~ the Fibonacci Spiral. The mathematical window of my brain has closed tight after schooldays..., but I will keep it open as I bump into interesting correlation with other blooms. Life has been guarded with interesting equations, on a simple note, we cry when sad, and we laugh when happy!....and has always been that enywhere.... CHEERS!!!!!!


    It would nice to botch it and having it going backwards. Huh.., like starting off as an old person and move backwards slowly into MOMMY'S belly. Sorry about the pollens Rosey! and for RAINNIE, you are always good with delicate points about life.... and don't go into difficult mathematical equations please. My add maths has gone rusty! Nice to know our sunflowers bloom about the same time MEREDITH, I bet yours is a lot bigger, yellower and nicer, because your place is nearer to the ancestral land of sunflowers.

    Have a nice day, looking forward to your exciting next post in Blotanical Blogs.
    ~bangchik and kakdah
    Putrajaya, MALAYSIA.

  15. How nice to be a single child in the family! I am not sure we'd see such great post if you had a field of sunflowers!

  16. I do agree with you TATYANA. We don't even look at faces in a crowd of thousands, but we can sit down with the loved ones, and talk about almost anything.... But our sunflower must be very lonely without peers... haha. ~bangchik

  17. Sunflowers make your day and great info!. Your post is really interesting.

  18. FJL... you always take the last train... haha. You are right about sunflower, it really make our day, compensating gloomy days when seeds refuse to sprout! ~bangchik


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