Jump to content
UltravioletPhotography

Idle Moments and Fibonacci Numbers


Andrea B.

Recommended Posts

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.

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.

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.)

erigeronSp_visFlash_20140805somesvilleME_25294fibonacci21.jpg

 

Note that there are no spiral truncations in the clockwise count.

erigeronSp_visFlash_20140805somesvilleME_25294fibonacci13.jpg

Link to comment

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:

 

leucanthemumVulgare_visFlash_20140726shoreCottageSwhME_24228pn02.jpg

 

erigeronSp_visFlash_20140805somesvilleME_25294.jpg

Link to comment

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.

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.

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.

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!

tripleurospermumMaritimum_uvBaadSB14_20140726_shoreCottageSwhME_24194dots.jpg

Link to comment

Please sign in to comment

You will be able to leave a comment after signing in



Sign In Now
×
×
  • Create New...