Thursday, 26 July 2012

Sunflower missing a spiral?

A while back Dr James Grime planted a sunflower in my backyard.

He was trying to raise awareness for the Turing's Sunflower project.

Well I'm pleased to report the potted sunflower is all grown up.

Slight problem though. We counted the seed spirals which supposedly should match with Fibonacci numbers.

In one direction got a match (34) but in the other direction we seem one short (54).

The seeds are notoriously hard to count though!

Have we got it wrong?

I've put a higher res version of the pic on Flickr.


  1. Check out Vi's third video on Fibonacci numbers She addresses cases where sometimes other number series show up. I've not counted your spirals yet, but it is possible you have a non-Fibonacci spiral.

  2. Counting the spirals in the middle (purple seeds in stead of green) I get 27 going right and 22 going left.

  3. 34 and 54 for me too. :(

    Bottom right quadrant is a bit tricky.

    Fingers crossed - hope it grows another spiral. :p

  4. I count 55.

  5. I count 54.

    Andrew, I looked over your pictures. I think you mis-drew spirals 50-54. In particular #51 shouldn't be there. 51 starts at the seed where 50 should start. After the first seed, the spiral it follows is actually the one marked 52. 52 then ends up pushing into 53, and 53 pushes into 54. Everything's back to normal at 55.

  6. Taking a cue from vihart's video...

    The answer lies with Lucas numbers starting with 8 and 6.

    8+6 = 14, 6+14= 20, 14+20 = 34, 20+34 = 54.

    If we're lucky the tighter spirals within the flower would be either 14, 8 or 6...

  7. I'm Jonathan Swinton who first suggested the Science Festival project and this is very exciting to see. A few points:

    I did my own estimate without looking at what anyone else got and I got...54.
    Maybe that's right of course but there are a couple of things I'd want to check. As Steven and Andrew make clear there is an ambiguity around Andrew's spiral 51 which could be resolved by moving the yellow ray floret out of the way. Also between Steven's spiral 39 and 40 it looks to me like there is a gap. It would be interesting to know if this is an artefact, a seed that has fallen out, or a genuine gap.

    In most varieties, the spiral patterns get clearer once all the yellow ray florets ('petals') have fallen off and in particular after all the tiny (actual) flowers have fallen off the tops of the seeds. So I am looking forward to seeing another photo in a few weeks...

    I'm not quite sure if Venky is being serious, but (sadly) since every pair of integers is in _some_ Lucas number sequence its not wise to ascribe too much significance to that.

    Vidad's observation of the inner spiral count is interesting too - would anyone like to produce an image of those counts? There is theory on what they should be if the outer counts are not Fibonacci.

  8. I checked this on a sunflower in my own garden, and I counted 55 on the inner spiral.

  9. Yeah, I'm a few years late, but I get 34 and 55:

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