How the sequence is built
The rule is simply F(n) = F(n−1) + F(n−2), seeded with F(0) = 0 and F(1) = 1. From those two starting values the whole infinite sequence unfolds. As the numbers grow, the ratio between consecutive terms converges on the golden ratio φ ≈ 1.618, which is why Fibonacci turns up in art, design and nature.