Fibonacci & Eigenvalues

Drag the slider to increase k. Watch the sequence grow exponentially, guided completely by the dominant eigenvalue λ₁ (The Golden Ratio).

Simulation Step (k) 2

2 15

x₂ =

1 1

1. True Sequence (f_k) 1

2. Eigen Approx (c₁λ₁^k) 1.17

Ratio (f_k / f_k-1) 1.0000

Golden Ratio (λ₁) 1.6180

Exponential Growth

f_k (True)

c₁λ₁^k (Approx)

Eigenvalue Convergence

Ratio f_k / f_k-1

λ₁ (1.618)