🌀Fibonacci Generator
The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21... Each term is the sum of the two preceding. Consecutive Fibonacci ratios converge to φ (golden ratio ≈ 1.61803).
- 1F(0)=0, F(1)=1, F(n)=F(n−1)+F(n−2)
- 2Binet: F(n) = (φⁿ − ψⁿ)/√5
- 3φ = (1+√5)/2 ≈ 1.61803
F(10)/F(9) = 34/21=1.619 ≈ φRatio converges to golden ratio
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Fun Fact
Sunflower seeds, pine cones, and shells exhibit Fibonacci patterns. The spirals in opposite directions are always consecutive Fibonacci numbers (commonly 34 and 55).
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