Speleotron said:
The petals thing is another Fibonacci myth, based on a very selective reporting, see this quote:
Wilson cites numbers of petals on flowers.
lily 3
violet 5
delphinium 8
mayweed 13
aster 21
pyrethrum 34
helenium 55
michelmas daisy 89
These examples associate with Fibonacci numbers. But Wilson neglects to mention these others:
many trees 0 This is a Fibonacci number. [3]
mustard, dames' rocket 4 Not a Fibonacci number.
tulip, hyacinth 6 Not a Fibonacci number.
starflower, eggplant 7 Not a Fibonacci number.
gardenia 8, 9 or 10 petals. 9 and 10 are not Fibonacci numbers.
Greek anemonie (various) 14 or 15 Not Fibonacci numbers.
black-eyed susan (some) 14 Not a Fibonacci number.
mountain laurel 10 Not a Fibonacci number.
gazania 16 Not a Fibonacci number.
https://www.lockhaven.edu/~dsimanek/pseudo/fibonacc.htm
For a start, Wilson is getting confused about petals and flowers - from mayweed onwards he's counting flowers not petals (they're all in the daisy family, where each "petal" is in fact a flower complete with sexual parts), and there's no reason which you should expect flowers to be part of the same sequence as petals.
The higher numbers in the second list are not necessarily the basal number of petals, they're varieties chosen for stamens having changed into extra petals, so again no reason to expect them to be part of a sequence. And Gazania is another daisy family plant, so the count there is of flowers not petals.
So it's pretty easy to debunk any theory that number of petals has anything to do with the Fibonacci sequence. It's more convincing when related to spirals. But even so, how meaningful is it to take a single number, or even two numbers, and say "this is a part of THIS sequence"?
But I suspect it all originates with a desire to find a divine order to things (or even any order). Musical notes were tied up with trying to unravel "the music of the spheres", and our western scale comes from dividing frequencies in simple ratios, then finding out you don't get quite the same answer depending on which order you do the divisions in, and making compromises ("The well tempered Clavier").