• Ultraviolet Photography

Idle Moments and Fibonacci Numbers

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#1 Andrea B.

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Posted 26 October 2017 - 15:33

After a rather long day sorting through 30+ years of accumulated US Income Tax forms and supporting documents, I found myself very late at night counting spirals on Asteraceae flower disks. I'm not sure exactly why all that tax data triggered a foray into the Fibonacci numbers of Asteraceae disk spirals but as the kids say -- whatever. It was fun. And it also proves that there is always something else to do when the North American summer has passed and there are no more wildflowers to document in UV.

In the attached examples you can see that it is not always easy to pick out a complete spiral on the flower disk. Either flowers have a mind of their own (...j/k...) or floral genetics and development are not always perfect. Anyway, I used some color overlay in PSE to highlight what I was attempting to count.

Goal: Enumerate spirals on flower disks to confirm that the counts are from the Fibonacci number sequence:
1 1 2 3 5 8 13 21 34 55 89 ...
Sub-goal: Ponder why this is true.

We can quibble over whether I have selected the correct spirals to count. Or whether a particular tiny floret belongs to this spiral or that spiral. But let's ignore minor details in the spirit of simple fun. :D

Shasta Daisy: The spirals were easy to pick out when counting counter-clockwise. Counting spirals clockwise, was rather difficult. No matter how I started, the spirals "piled up" eventually.
Attached Image: leucanthemumVulgare_visFlash_20140726shoreCottageSwhME_24228fibonacci21.jpg

Note how spiral #4 is truncated in the clockwise count. Also note how the spirals seem to be lost in the outer area of the disk where the florets have bloomed.
Attached Image: leucanthemumVulgare_visFlash_20140726shoreCottageSwhME_24228fibonacci34.jpg

Fleabane: For this flower the clockwise count was easy and the counter-clockwise count messy.
(I also had a bit of Fun with Fonts.)
Attached Image: erigeronSp_visFlash_20140805somesvilleME_25294fibonacci21.jpg

Note that there are no spiral truncations in the clockwise count.
Attached Image: erigeronSp_visFlash_20140805somesvilleME_25294fibonacci13.jpg
Andrea G. Blum
Often found hanging out with flowers & bees.

#2 Andrea B.

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Posted 26 October 2017 - 15:37

In case you would like to perform your own spiral count, here are the two disks unmarked. Alternately go find a pinecone or a pineapple and count its spirals. :lol:

Attached Image: leucanthemumVulgare_visFlash_20140726shoreCottageSwhME_24228pn02.jpg

Attached Image: erigeronSp_visFlash_20140805somesvilleME_25294.jpg
Andrea G. Blum
Often found hanging out with flowers & bees.

#3 Alaun


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Posted 27 October 2017 - 06:59

The outer spirals take the next no.?


Attached Images

  • Attached Image: fibo_AB.jpg


#4 Andrea B.

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Posted 27 October 2017 - 16:56

Thanks, Werner!
I was beginning to think nobody was reading this little off-topic post. :D

When I was working on these, I ran out of patience (it was very late) and did not count the outer (already bloomed) floret bands as you did so nicely. Now I wonder if the petal count is a Fibonacci number?

Isn't nature wonderful !!
(slang: "Ain't nature just grand !!")


Here is a Sea Chamomile (Tripleurospermum maritimum) that I had some trouble with while trying to find spirals. It turned out to be easier in this case to use the UV version because the floret tips were UV-bright. There is one "trapped" or "truncated" spiral highlighted in green.
Attached Image: tripleurospermumMaritimum_uvBaadSB14_20140726_shoreCottageSwhME_24194fibonacci21.jpg

Sea Chamomile center crops.
You can see that the lower right area of the center disk is irregular due to some kind of growth problem or perhaps some damage. There also seem to be a couple of florets missing on the left side.
Attached Image: tripleurospermumMaritimum_visFlash_20140726_shoreCottageSwhME_24188spiralsCenter.jpg

Much easier to find spirals in the UV version.
Hint: start on the outer edge and work your way inwards.
Attached Image: tripleurospermumMaritimum_uvBaadSB14_20140726_shoreCottageSwhME_24194fibCe ter.jpg

Connect the dots. :lol: :rolleyes:
I see that there is one half-white, half-yellow dot. Someday when I have absolutely nothing else to do, I might correct that!
Attached Image: tripleurospermumMaritimum_uvBaadSB14_20140726_shoreCottageSwhME_24194dots.jpg
Andrea G. Blum
Often found hanging out with flowers & bees.