Saturday, May 26, 2012

[jules' pics] pink

It's not just Japan. Even in Britain two shades of pink can be found...
pink flowers

pink flower

Posted By Blogger to jules' pics at 5/26/2012 09:07:00 AM


Steve L said...

Hey, looking at the bottom flower here, it looks like about 18 petals. That's not a Fibonacci sequence number. I dunno much about plants or about Fibonacci sequences, but I've seen comments all over the place that Fibonacci sequences can be observed everywhere in nature, especially in plants. Is it worth noting that there are plenty of counter-examples?

andrewt said...

Actually the 18 things that look like petals, aren't petals at all, my botany is rusty but daisies (Astererace) have a composite flower, and the things that most of us would call petals are ray florets and the petals are tiny things in the centre.

People certainly give ray florets on daisies as an example where the fibonacci numbers appear but if you go out to the wild (or the garden) and count you'll quickly discover the number isn't constant within a population. I guess the mean might tend to be be near a fibonacci number but I haven't seen hard evidence of this.

James Annan said...

There are well-known exceptions to the Fibonacci tendency, but daisies do seem to be mentioned as a typical example. Interestingly, 18 is a Lucas number (2,1,3,4,7,11,18...). Of course individual flower (heads) may be abnormal anyway.

Steve L said...

Cool! I had never heard of Lucas sequences. I've finally had time to read a bit. My botany has completely corroded into dust and blown away, so I learned a couple of things here. Thanks.

andrewt said...

You are sounding like a typical theoretician James - rather than actually count the rays on a few few daisies - you instead bring up Lucas numbers - throw in enough sequences and you'll have all small integers covered and have no need to go near actual data.

FWIW googling does suggest there is good reason to believe the development of the structure of the composite flowers in daisy could result in ray counts near members of fibonacci and similar additive series.

But does it actually occur? There are vast number of daisy species but sunflowers seem the most often cited. Googling turned up ray counts for a sample of 6 US sunflower
species here:

8-20 rays
10-15 rays
5-8 rays
8-15 rays
10-20 rays
11-20 rays

which doesn't rule out modes near fibonacci numbers, but indicates considerable variation.

Carrick said...

That is pretty cool. Until looking at the wiki entry, I also had no idea they would have a closed form formula, let alone have an extension to the complex plane (n -> z).

That'll play with your head.

James Annan said...

Carrick, shame that scientists often seem to miss out on the fun bits of maths! One of my sneakier maths teachers set me off on the Collatz conjecture once - only he didn't give me the name and there wasn't any meaningful internet in those days...surprisingly enough, I didn't get very far.

Andrew, 18 is also the only positive number that is twice the sum of its digits :-)