Regarding the composite flowers and seed heads, Leonardo da Vinci was the first to suggest that the adaptive advantage of the Fibonacci pattern is to maximize exposure to dew. Current thinking supports this interpretation. Phyllotactic architecture optimizes access to moisture, rainfall and sunlight.
The most famous example is the sunflower head. This phyllotactic pattern creates an optical illusion of criss-crossing spirals. In the botanical literature, these designs are described by the number of counter-clockwise spirals and the number of clockwise spirals. These also turn out to be Fibonacci numbers. In some cases, the numbers appear to be multiples of Fibonacci numbers because the spirals consist of whorls.