Packaging is the key!!! Nature chooses the arrangement that wastes the least amount of space. So you would think that squares would be packaged most closely in a square array, and circles would be packaged in a hexagonal array, but seed heads are not in the shape of a hexagon! This is because the hexagon shape does not take into consideration how the leaves should be arranged around the stem or how to pack a seed head with seeds that grow in size.
We can see from the examples like the sunflower that nature uses the same pattern to place seeds, leaves, and petals. Nature uses a fixed angle to produce its optimal design. So, if a seed is positioned on a seed head, and then is pushed out by in a straight line by other seeds, it will retain the original angle on the seed head. It does not matter how big the seeds or the seed head becomes, the seeds will always be packed uniformly.
The angle that
nature uses is Phi,1.618. For example, in the placement of leaves
on a steam, there are Phi leaves per turn. This gives the best packaging
and the maximum exposure to light for each leaf! It also allows the
most exposure to rain. The plant itself is based upon the golden
number. The Fibonacci numbers are the best whole number approximations
to the golden number and, we discussed earlier how the golden ratio and
Fibonacci numbers are related.
Here are links to show what would happen to seeds if nature chose an angle other than Phi!