4
Fig 17 and Fig18 show a 3° window, 1.5° either side of 137.5° still showing Fibonacci numbers while employing different angles. Their symmetry is morphing in both directions away from 137.5° towards static rationality away from dynamic irrationality.
Fig 17
Fig 18
Fig 17 shows the situation 1° short of 135°, the point at which there will be 8 petals repeating. Fig 18 shows the situation 5° short of 144°, when there will be 5 petals repeating.
5 and 8 are Fibonacci numbers, symmetrical anchors standing at either end of a band within which both numbers are displayed, along with the numbers below them.
It makes sense, accepting the perceived angle hypothesis, that the Fibonacci numbers in plants should derive from the angles employed rather than the other way around.
Figs 19, 20 and 21 show two members of the daisy family, each with 13 petals, and between them 13 iterations at 137.5°, which group into 5 pairs and 3 singles. It is easier to see this after looking at Fig 23 on page 5 [cyberflowers]. The two petal arrangements differ from each other and from the diagram. The seed heads also show variation.
Fig 19
Fig 20
Fig 21
In Fig 22 a beautiful, almost quadrilateral, sunflower seedhead with good tight packing but more spirals than might be expected.
Fig 22
These pictures are a reminder that the phi ratio is irrational, the roughly 137.5° angle produced by its division of the circle is also, and results in the field add another dimension of uncertainty.
Flowers which are using the divergence angle of 137.5° overrun or underrun. A 22 petalled daisy is neither very uncommon, nor does it mean that the flower is using a different system from one with 21 petals, or indeed 20.

Close can be good enough.