6
Fig 24 displays a count of the number of appearances made by each color in the diagrams in Fig 23 on page 5 [cyberflowers]. Where the Fibonacci numbers occur there are only two colors used in the diagram. These are the points of best balance, but in the earlier iterations best is sometimes not good enough.
Fig 24
Fig 25
13/21=0.6190
8/13=0.6154
5/8=0.6250
3/5=0.6000
2/3=0.6667
1/2=0.5000
1/1=1.000
0/1=0
Fig 25 shows the ratios fluctuating towards their distant goal.
It may be that employing the phi angle is less competitive in its early iterations, and is responsible for fewer 3 and 5 petalled flowers than mutual repulsion. The eighth iteration is where the [roughly] 137.5° divergence angle starts to come into its own for petals, and 13 petalled flowers, like the cheerful ragwort in Fig 26, seem to be more common than those with 8. The seedhead shows some far from perfect packing.
Fig 26
Fig 27
In Fig 27 the numbers in rings, outside the frame, refer to the numerical intervals between primordia on the same spiral. The numbers without rings, inside the frame, refer to the order of appearance of the primordia.
The primordia, while the distances between them increase with growth, maintain their divergence angle. This suggests a steady growth rate, just sufficient mutual repulsion to keep the elements separate, and an aiming mechanism yet to be described.
When leaves spiral around a stem the pattern of growth is described by a fraction. Fig 28 shows a cycle of 8 leaves and 5 revolutions around the stem. This is described as a 5/8 phyllotaxis.

1800° [5 circles] divided by 8 gives 225°. This is the reflex angle, and accounts for the distance travelled along the spiral.

Fig 29 shows the same leaves, appearing in the same order, in the same places. This time the angle is 135°, and the process is completed after 3 [still a Fibonacci number] circles [1080°]. Looking at it this way, might the phyllotaxis be described as 3/8?

It is interesting to see how these Fibonacci numbers are still expressed in a situation of rational symmetry 2.5° away from the golden angle of 137.5° [roughly].
Fig 28
Fig 29
Fig 30
Fig 30 shows how plants might employ oppositeness to a perceived angle of 45° to provide a divergence angle of 135°. And also how oppositeness to 135° might provide a divergence angle of 225°. But why go to the trouble?
Fig 31
Compare Fig 31 which has the first 8 iterations in black and the 9th one red, all at 137.5°, with Figs 28 and 29 in which the 9th leaf is directly above the 1st. That's the difference 2.5° makes.