3
The blackberry is another reminder that the question is not only how do Fibonacci numbers appear in plants, but how don't they appear?
The blackberry...
Fig 12
Fig 13
Fig 14
...is a plant in a hurry. It grows fast and shows many variations: 3 and 5 leaf groups: different divergence angles: different orders of primordium appearance: different levels of siamesing. But an underlying pattern is discernible. And once again this 5 is not a Fibonacci 5.
The size of blackberry leaves indicates the order of appearance of the primordia. Stem lengths show the relative duration of the pauses between the appearances of the primordia.
In Fig 12 a is followed by b to the right with a divergence angle of roughly 60°. c, opposite to b, maintains the angle. Then d grows opposite to c on another axis, and is followed by e opposite to b. d and e appear so quickly after their predecessors that siamesing is common. Fig 13 goes the same way. Fig 14 does it differently.
Fig 15 shows half siamesing. In Fig 16 the two lowest leaves are almost completely enveloped by the two above. Nevertheless the leaf orders of appearance can still be seen, both left and right handed. As can the directionality of d and e in both plants despite the siamesing.

The larger the angle of divergence the greater the chance that leaves will siamese. Maybe this is what leads to 3 leafed groups. Many palmate leaves appear to have developed from similar five leaf clusters.
Fig 16
Fig 15
A generic blackberry program might be:

1 a straight ahead
2 Pause
3 b to one side at x°
4 Short pause
5 c opposite to b at x°
6 Shorter pause
7 d opposite to b or c
8 Even shorter pause
9 e opposite to c or b
Those plants which exhibit elements in numbers which really are from the Fibonacci series have employed oppositeness to a perceived angle of roughly 42.5° and simplified their algorithm to:

1 a straight ahead
2 next at roughly 137.5°
3 goto 2

The level of accuracy required is less demanding, and less unlikely, than the numbers of the Fibonacci series at first suggest.