The Fibonacci sequence, or how nature counts

There’s a pattern that keeps showing up across living things: the spiral of seeds in a sunflower, the arrangement of scales on a pinecone, the shell of a nautilus. That pattern has a name: the Fibonacci sequence.

The sequence

Each term is the sum of the two before it:

Which gives: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

The golden ratio

Divide two consecutive terms and the result converges to a remarkable constant, the golden ratio $\varphi$:

This is the proportion nature seems to “prefer” for organizing growth — it lets seeds or leaves pack together without ever overlapping perfectly, maximizing exposure to light or available space.

A tiny script to check the convergence:

def fibonacci(n):
    a, b = 0, 1
    for _ in range(n):
        a, b = b, a + b
    return a

for n in range(2, 12):
    print(fibonacci(n + 1) / fibonacci(n))

Every time I walk through a forest, I think about this formula quietly running behind every leaf. A good reminder that math is never too far from the living world.