1. For an explanation of why the Fibonacci numbers appear in phyllotaxis, see Peter S. Stevens, Patterns in Nature (Boston: Little, Brown, 1974).
(also, see Ron Knott's Fibonacci Series page for lots of fascinating information on Fibonacci numbers.)

2. For a thorough discussion of Penrose tiles, Ammann bars, "musical" sequences, and related matters, see Grunbaum and Shepard, Tilings and Patterns (New York:Freeman , 1987).