Sunflower mosaic geometry?

[Tony Halmarack]

I'm tiling the kitchen and my wife suggested a sunflower mosaic as part of
the splash-back. I did a search for sunflower images, which lead in turn to
some awed consideration of the Fibonacci sequence of seed distribution in
flower heads.
I know little of math or geometry and being of mature years, I allowed
myself to be lulled into thinking that I 'd effectively escaped the
subjects. Next thing I know, I'm snared.

Please can anyone tell me what branch of geometry deals with 2D
representations of seed distribution in a flower head, based on the
Fibonacci sequence?

Are there documents that shows the way to construct a geometrical drawing
of seed distribution of this type?

I saw an example of a distribution pattern made up of dots, with spiraling
lines running dot-to-dot. This was an example produced by software on the
Mac. I have a PC, so I drew a copy as best I could but I don't like what
happens in the middle, in relation to a mosaic layout. The polygons
produced by the intersecting spirals become very elongated and petal like
near the centre which doesn't lend itself very well to producing a seed
like visual effect with tiles.
I'd be grateful for any advice you can give.

Regards,

--
Tony Halmarack