After 3 hours with google, a method for generating these spiral quadrilaterals was not found.
They cold be measured from plants, or traced on the Fibonacci script?

I did locate professor Scott Hotton's gif, (and several mathematically esoteric papers with hyperbolic geometry.)
http://scotton.freeshell.org/phyllo/lattice_5_8.gif
The central "beginnings" and expansion factor are unclear.

Perhaps a rotated scaled Fibonacci curve??

As time permits, I may try some curve fitting in MoI.
Or read some of the papers, including finding the "center point" of "pinecone" curves.
It is an interesting homework assignment:-)

- Brian

This site seems promising:
http://www.math.smith.edu/~phyllo/About/Lattices/SpiralLattices.html