Fibonacci recurrence (golden ratio)

Layer 0 — Mathematicsin the difference-and-functional-equations subtree

F_n+1 = F_n + F_n-1 with F_0 = 0, F_1 = 1. Closed-form Binet F_n = (φ^n - ψ^n)/√5 where φ = (1+√5)/2 golden ratio. Limiting ratio F_n+1/F_n → φ. Appears in phyllotaxis, art (Parthenon), continued fractions ([1;1,1,...]).

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