Generate Fibonacci sequences with custom starting values and observe the convergence to the golden ratio.
The Fibonacci sequence starts with 0 and 1, each subsequent number is the sum of the two preceding ones. F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2).
The ratio of consecutive Fibonacci numbers F(n)/F(n-1) converges to the golden ratio Ο β 1.61803 as n increases.
Fibonacci numbers appear in sunflower seed spirals, nautilus shells, tree branching, pine cone spirals, and many other natural patterns.
Fibonacci numbers are used in financial market analysis (Fibonacci retracement), algorithm design (Fibonacci heap/search), and art composition.